Ramil Paper

DETERMINATION OF FORMING LIMIT CURVES OF STEEL PIPES FOR HYDROFORMABILITY EVALUATION OF AUTOMOTIVE PARTS

RAMIL KESVARAKUL

A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE DEGREE OF

MASTER OF ENGINEERING IN AUTOMOTIVE ENGINEERING (INTERNATIONAL PROGRAM)

INTERNATIONAL COLLEGE KING MONGKUT’S INSTITUTE OF TECHNOLOGY LADKRABANG

2010 KMITL-2010-IC-M-004-007

COPYRIGHT 2010

INTERNATIONAL COLLEGE

KING MONGKUT’S INSTITUTE OF TECHNOLOGY LADKRABANG

NATIONAL SCIENCE AND DEVELOPMENT AGENCY

Thesis Title: Determination of forming limit curves of steel pipes for

hydroformability evaluation of automotive parts

Student: Ramil Kesvarakul Student ID: 51061914

Degree: Master of Engineering

Programme: Automotive Engineering

Year: 2010

Thesis Advisor: Dr. Monsak Pimsarn Dr. Suwat Jirathearanat

Assoc.Prof. Naoto Ohtake

ABSTRACT

The aims of this research are to establish the forming limit curve (FLC) of tubular material

low carbon steels commonly used in Thai industry, verify these FLCs with real part forming

experiments, and compare these experimentally obtained FLCs against analytical ones available in

FEA software database. A self-designed bulge forming apparatus of fixed bulge length and a

hydraulic test machine with axial feeding are used to carry out the bulge tests. Loading paths resulting

to linear strain paths at the apex of the bulging tube are determined by FE simulations in conjunction

with a self-compiled subroutine. These loading paths are used to control the internal pressure and

axial feeding punch of the test machine. In this work a common low carbon steel tubing grade STKM

11A, with 28.6 mm outer diameter and 1.2 mm thick is studied. Circular grids are electro chemically

etched onto the surface of tube samples. Subsequently, the tube samples are bulge-formed. The

forming process is stopped when a burst is observed on the forming sample. After conducting the

bulge tests, major and minor strains of the grids located beside the bursting line on the tube surface

are measured to construct the forming limit curve (FLC) of the tubes. The forming limit curves

determined for these tubular materials are put to test in formability evaluations of test parts forming in

real experiment.

It was found that the tool geometry can keep the strain ratio constant is not dependent on the

thickness but only on OD of the tube, as in equations 𝐿 = 𝑂𝐷 and 𝑟 = ×. . The experimental

FLDs have predicted failures in forming process consistently with the real experiments. The

experimentally obtained forming limit curves (determined following STKM 11A) differ from

empirical one (from FEA software) and analytical one by about 0.02339 and 0.15736 true strain

respectively at FLD0, the corresponding plane strain values.

ACKNOWLEDGEMENT This thesis could not be completed without the assistance of many persons to whom I would

like to express my sincere appreciation.

First, I would like to sincerely thank my advisor, Dr. Suwat Jirathearanat, who has given me

many helpful suggestions, useful advice during the undertaken research.

I would also like to sincerely thank Asst. Prof. Dr.Monsak Pimsarn for kind advising and

helping, and Assoc. Prof. Naoto Ohtake for the suggestion of oxide analysis.

Moreover, I would like to show gratitude to the National Metal and Materials Technology

Center (MTEC) laboratory for providing the laboratory equipments and instruments as well as

financial supporting.

I am grateful to the National Science and Technology Development Agency (NSTDA), which

provided the full scholarship for studying in the master program.

Finally, I am very grateful to my family for all love, caring, understanding and motivation

throughout my life.

Ramil Kesvarakul

III

CONTENTS

Page

ABSTRACT I

ACKNOWLEDGMENTS II

CONTENTS III

LIST OF TABLES VII

LIST OF FIGURES VIII

CHAPTER 1 INTRODUCTION

1.1 Significance and Background 1

1.2 Objectives 2

1.3 Scopes 2

1.4 Expected Results 2

CHAPTER 2 THEORY AND LITERATURE REVIEWS

2.1 Introduction to Tube Hydroforming (THF) 3

2.2 Material Property 5

2.2.1 Stress 5

2.2.2 Strain 5

2.2.3 Tensile Test 6

2.2.4 The Engineering Stress-Strain Curve 6

2.2.5 Anisotropy 9

2.3 Tubular blank 10

2.4 Strain-based forming limit curve 11

2.4.1 Formulation of plastic instability criteria 14

2.4.2 FLC obtained by Finite Element software: DYNAFORM 20

2.5 Ductile fracture criterion 21

2.6 Effect of non-linearity of strain path 24

IV

CONTENTS (CONT.)

Page

CHAPTER 3 RESEARCH METHODOLOGY

3.1 Numerical Investigation 27

3.1.1 Test die insert design 27

3.1.2 Determination of loading paths by FE-simulations 31

3.2 Experimental Investigation 36

3.2.1 FLC testing apparatus 36

3.2.2 THF Test Specimens 37

3.2.3 Hydraulic press 38

3.2.4 Pressure system, Hydraulic cylinders and punches 39

3.3 Grid measurement 39

3.3.1 Digital Microscope 39

3.3.2 Grid Curvature 40

CHAPTER 4 EXPERIMENTATION AND RESULTS

4.1 Tube Hydraulic Bulge Test 43

4.1.1 Forming limit experiments with axial feeding 44

4.1.2 Forming limit experiments without axial feeding 49

4.1.3 Forming limit of welded seam 51

4.2 Grid Measurement 52

4.3 Construction of the Forming Limit Curve(FLC) 53

CHAPTER 5 COMPARISON AND VERIFICATION

5.1 Empirical FLC, Analytical FLC and Experimental FLC 59

5.2 Verification of Experimental FLC 62

5.2.1 Verification of Experimental FLC with actual bulge test

load path 62

5.2.2 Verification of Experimental FLC with a real automotive part 64

V

CONTENTS (CONT.)

Page

CHAPTER 6 CONCLUSION AND SUGGESTIONS

6.1 Conclusions 66

6.2 Suggestions for Future Work 67

REFERENCES 68

APPENDIX 70

Appendix A: International Conference: Determination of forming limit

curves of tubular materials for hydroformability

evaluation of automotive parts 70

Appendix B: Determination of forming limit curves of tubular 79

Appendix C: Tooling schematic 87

BIOGRAPHY 95

LIST OF TABLES

Table Page

3.1 Design of simulation matrix 28

3.2 A series of simulation 29

3.3 Simulation results 29

3.4 A series of simulation, L/OD=1 and rd/t=15 30

3.5 Result of Simulation, L/OD=1 and rd/t=15 31

4.1 Grid curvature 52

LIST OF FIGURES

Figures Page

2.1 Schematic illustration of the hydroforming of a bulge in a tube 3

2.2 Example tube hydroformed parts: a 2004 Ford F-150, chassis frame 4

VI

LIST OF FIGURES (CONT.)

Figures Page

2.3 Components of stress on element (Hosford and Caddell, 2007). 5

2.4 Typical tensile specimen (Marciniak et al., 2002). 6

2.5 Load-extension diagram for tensile test (Marciniak et al., 2002). 6

2.6 Engineer stress-strain curve (Marciniak, Z.et al. 2002). 7

2.7 The elastic behavior of typical tensile test (Marciniak, Z.et al. 2002). 8

2.8 Diagram used to determine the proof stress in a material (Marciniak, Z.et al. 2002). 8

2.9 Measurement of r value by tensile specimen from three directions (ASTM, 1998). 9

2.10 Electric resistance welded pipe process. (PIPING HANDBOOK, 2000) 10

2.11 Electric Resistance Welding (ERW) Tube 11

2.12 Three basic zones - red, yellow, and green of Forming limit diagram. 12

2.13 FLD with different principle strain ratio 12

2.14 Schematic figure of the subtangent of a stress strain curve as necking occurs.

(Yeong-Maw Hwang. 2009) 15

2.15 Flow chart for determining the critical major and minor principal strains. 18

2.16 The forming limit curve and yield locus with Hill’s non-quadratic yield function. 19

2.17 The forming limit curve with Keeler’s formula. 20

2.18 Forming limit diagram obtained experimentally for a STKM-11A tube

(Li-Ping Lei, 2002). 22

2.19 Variations of σ σ⁄ and dε dε⁄ with respect to strain ratio β

(Li-Ping Lei, 2002). 23

2.20 Determination of C1 and C2 for a STKM-11A tube (Li-Ping Lei, 2002). 23

2.21 Influence of strain path on the FLC (adapted from Graf and Hosford, 1993). 24

3.1 Schematic diagram of the test die insert parameters 27

3.2 The formed part show in half model 28

3.3 testing die insert geometry 31

3.4 Feeding distance (mm) with time(s) 32

3.5 Internal Pressure (bar) with time (s) 33

3.6 Feeding distance (mm) with Internal Pressure (bar) 34

3.7 Simulation results with four strain ratios

(ξ = ε ε⁄ ) -0.1, -0.2, -0.3, -0.4 and no feeding 35

VII


Figures Page

3.8 Different strain paths investigated 36

3.9 The experimental apparatus for bulge tests without axial feeding 36

3.10 The experimental apparatus for bulge tests with axial feeding 37

3.11 Schematic diagram of the experimental apparatus for bulge tests 37

3.11 Circular grids with a diameter of 2.5mm 38

3.12 THF Test Specimens 38

3.13 Hydraulic press and CNC controller 38

3.14 CNC controller used to control internal pressure and axial punches 39

3.15 Digital Microscope (Dino-Lite) 39

3.16 The deformed grids measured using Dino Capture Software 40

3.17 r is meridian radius of curvature at the pole 40

3.18 r is circumferential radius of curvature at the pole 40

3.19 A photo of bulged tube for curvature measurement 41

3.20 Approximation of the curve by CAD software 41

4.1 Apparatus with feeding tooling set 42

4.2 Apparatus without feeding tooling set 42

4.3 Loading path, Feeding distance (mm) and Internal pressure (bar) with time(s) 43

4.4 Loading path, Feeding distance (mm) with Internal Pressure (bar) 43

4.5 Loading path, Feeding distance (mm) with Internal Pressure (bar) 44

4.6 Results of the formed product for different strain paths. 44

4.7 loading path and Results of the formed product of different deformed state-Set1 45




4.11 Loading path, Internal Pressure (bar) with times(s) 49

4.12 Results of the formed product without axial feeding. 49


4.14 The specimens that burst at welded seam and corresponding load path. 51

4.15 Measure zone covering ±45 degrees from welding seam 53

VIII


Figures Page

4.16 FLC with the major and minor strains of all specimens

covering ±45 degrees from welding seam 52

4.17 The major and minor strain with degree from welding line of Set4 54

4.18 Set1 strain path at 30 degree 55


4.20 Set3 strain path at 22.5 degree 56

4.21 Set4 strain path at 27.5 degree 57


4.23 The Experimental FLD and forming limit curves (FLC) of STKM 11A tubes 58

5.1 Comparison of predicted forming limit strains with the experimental

forming limit strains for low carbon steels STKM 11A. 59

5.2 Effects of the r value on the forming limit curve with Hill’s non-

quadratic yield function. 60

5.3 Effects of the n value on the forming limit curve with Hill’s non-

quadratic yield function. 60

5.4 Effects of the t value on forming limit curve with Keeler’s formula. 61

5.5 Effects of the n value on the forming limit curve with Keeler’s formula 62

5.6 Results of Comparison for experiment and numerical simulation 63

5.7 A fuel filler pipe geometry. 64

5.8 A final product of fuel filler pipe. 64

5.9 A simulation model of fuel filler pipe. 65

5.10 Comparison of predicted forming limit strains with measured experimental data. 65

CHAPTER 1

INTRODUCTION

1.1 Significance and Background

Transportation of people and goods has always been one of the sectors that consume most

of energy resources and continuing to increase the consumption level at a rapid rate. Design and

production of high strength-to-weight ratioed automotive parts is now encouraged or even

enforced in most developed countries. Tube hydroforming technology is a promising new

forming process that produces tubular automotive parts with significant weight reduction.

Tube hydroforming is a tubular material-forming process that uses a pressurized fluid in

place of hard tooling, i.e. punch, to plastically deform a given blank material into a desired shape.

With this technique, more complex shapes with increased strength and reduced weight can be

manufactured as compared with stamping, forging or casting processes

The forming limit diagram (FLD) of tubular materials should be established, because it

clearly shows the formability of the hydraulic forming processes. A few studies concerning the

loading paths or the forming limit of tubes and sheets have been reported. For example, Jieshi

Chen (2009) study Sheet metal forming limit prediction based on plastic deformation energy, the

sheet metal forming limit is calculated by fitting curve from experimental data. The forming limit

curves determined for these sheet materials were put to test in formability evaluations of test parts

forming in both real experiment and numerical simulation that in this study he selected sheet

material ST14 with 0.8 and 0.85 mm thick. Yeong-Maw Hwang (2008) used bulge tests to

establish the forming limit diagram (FLD) of tubular material AA6011. Then he compared it with

the forming limits from analytical FLCs using the n values obtained by tensile tests and bulge

tests. E. Chu and Yu Xu (2008) showed work done by investigators who investigated the

prediction of forming limit diagrams (FLDs) for tube hydroforming of 6061-T4 seamless

extruded tubes.

From the literatures reviewed, it is clear that experimental determination of FLC using a

hydraulic bulging tube apparatus is necessary for accurate tube hydroforming part and process

design. So far, a consistent conclusion for forming limit theorems of tubular materials has not

been established and the forming limit diagram for STKM 11A tubes has not been found.

2

Therefore, this work aims to develop a capability to experimentally determine forming

limit curves (FLC) of tubular materials available in Thailand. In this work, hydraulic forming

machines are developed, experiments of bulge tests with and without axial feeding are carried out,

loading paths leading to the linear strain paths at the pole of the forming tube are determined by

FEA and are used to control the internal pressure and axial feeding in the forming limit

experiments. The experimentally obtained forming limits are later compared with some analytical

and empirical FLCs. A commonly available low carbon steel tubing, STKM 11A, is chosen to be

the target material in this study.

1.2 Objectives

1.2.1 To design a tube bulge forming apparatus to carry out tube hydraulic bulge test.

1.2.2 To determine the forming limit curve (FLC) of tubular material low carbon steels

commonly used in Thai industry

1.2.3 To verify the forming limit curve (FLC) with real part forming experiments for

actual applications.

1.3 Scopes

1.3.1 The designed bulge forming apparatus is to be used with MTEC hydroforming

system, maximum pressure 1000 bars, 200 tons hydraulic press.

1.3.2 The test tooling is to be designed for a material low carbon steel tubing

commonly used in Thai industry, namely STKM 11A with 1.2 mm thickness and

28.6 mm outer diameter.

1.3.3 Finite element software (DYNAFORM) is to be used for design tooling and

loading curve.

1.3.4 A real tubular part hydroforming experiments (Fuel filler) is to be used to verify

FLCs

1.4 Expected Benefits

1.4.1 Being able to use the forming limit curve (FLC) for tubular formability

evaluations accurately.

1.4.2 Useful the forming limit curve (FLC) that can be used to further develop THF

processes in the automotive industries.

CHAPTER 2

LITERATURE REVIEWS

2.1 Introduction to Tube Hydroforming (THF)

Tube hydroforming is a tubular material-forming process that uses a pressurized fluid in

place of hard tooling, i.e. punch, to plastically deform a given blank material into a desired shape

as depicted in Figure 2.1. During a hydroforming process, a tube is placed in the closed cavity of

a forming die. The ends of the tube are sealed by the axial punches. The axial punches are

necessary to seal the end of the tube to avoid pressure losses and to feed material into expansion

regions. After the ends of the tube are sealed, the hydraulic fluid is injected into the inner of the

tube and the tube is formed to conform the shape of the die cavity. They should feed the material

into the deformation zone in a controlled way, and in synchronization with internal pressure, i.e.

pressure versus time and axial force versus time should be controlled and coordinated. Tube

hydroforming process has drawn increasing attention in the automotive industries due to its

several advantages comparing with the conventional forming process (stamping, forging or

casting processes), such as reduction of the weight of components and overall number of

processes and more complex shapes with increased strength as show in Figure 2.2.

Figure 2.1 Schematic illustration of the hydroforming of a bulge in a tube

The first patented hydroforming application was obtained by Milton Garvin of the

Schaible Company of Cincinnati, Ohio, for producing kitchen spouts in the 1950s. Since the

1990s, hydroforming has made an impactful comeback due to the advancements in computer

controls, hydraulic systems and recently developed process and part design guidelines, and

various forged or stamped structural parts have been replaced by parts formed with tube

Dies Insert blank Seal

Pressurise and feed Final component

4

hydroforming technology (THF). Substantial weight and cost savings were realized with

hydroformed steel parts because of the part consolidation, less post-forming processes (i.e.,

joining such as welding and piercing) and initial thinner material thickness opportunities

(Dohmann, 1991; Koç, 2001; Murray, 1996 and Morphy, 1997).

Figure 2.2 Example tube hydroformed parts: a 2004 Ford F-150, chassis frame

In this study, focus is placed on the straight tube hydroforming process. In the straight

tube hydroforming process, axial force is always applied at the ends of the tube simultaneously

with the internal hydraulic pressure. Therefore, the material is fed into the deformation zone

during the forming process more expansion and less thinning. For the straight tube hydroforming

process, three characteristic failure modes, i.e., buckling, wrinkling, and bursting, are involved.

Buckling failure, which induces if high axial force acts on the beginning of the process, is a

function of the tube parameters and it is easy to be estimated in theoretical terms. Wrinkling

failure, which occurs in the expansion zone if the axial feeding is too high, sometimes can be

eliminated again by increasing the internal pressure during the final stage of the hydroforming

process. Bursting failure occurs as a result of excessive high internal pressure. By contrast with

buckling and wrinkling failure, bursting failure is irrecoverable. In order to obtain the final sound

hydroformed product, it is necessary to study the forming limit diagram of the straight tube

hydroforming process to optimize the forming process, and to reduce and finally eliminate the

costly die try-out in hydroforming process design.

5

2.2 Material property

For the sheet material, the ability to transform shaped, it called “formability”, should also

be considered. To assess formability, we can know behavior of the sheet from mechanical tests. In

sheet metal forming, we are interest two principles that are elastic and plastic deformation.

2.2.1 Stress

Stress is define as force, F, at a point

AF

(2.1)

Where A is the area at force action

In Figure 2.3 as show the components of stress. The normal stress is the force

acting normal to the plane. It may be tensile or compressive. The shear stress component is the

force acts parallel to the plan (Hosford and Caddell, 2007).

Figure 2.3 Components of stress on element (Hosford and Caddell, 2007).

2.2.2 Strain

Strain is total deformation in body, when the points in body are displaced by

deformation, which can be divided 2 types that are elastic strain and plastic strain. The elastic

strain means when the shape is deformed no force acting, element in body will move back to

origin shape. But for the plastic strain when unloading material holds permanent deformation. We

identify the plastic deformation by equation (2.2)

6

0

lnll

(2.2)

Where l Final length

0l Original length

2.2.3 Tensile Test

This is typical of a number of standard test specimens. A tensile test specimen is

shown in Figure 2.4. The initial thickness is 0t and the length of tensile test specimen that is a

smallest amount four times the width, 0w . The load on the specimen, F , is measured by a load

cell in the testing machine. The gauge length 0l is monitored by an extensometer in the middle of

the specimen and the change in width is measured by a transverse extensometer. During the test,

load and extension will be recorded in a data acquisition system. (Marciniak et al., 2002).

Figure 2.4 Typical tensile specimen (Marciniak et al., 2002).

2.2.4 The Engineering Stress-Strain Curve

Figure 2.5 shows load-extension diagram for a tensile test. The elastic extension

is so small that it can’t be seen. The initial yield load, yF , is plastic deformation commence

begin. During this part of the test, the cross-sectional area of specimen decreases while the length

increases; the load maximum, maxF , was a point reached when the strain-hardening effect

balanced the rate of decrease in area.

F

F

7

Figure 2.5 Load-extension diagram for tensile test (Marciniak et al., 2002).

The engineering stress-strain curve obtained by the initial cross-sectional area,

000 twA , and the extension by 0l . The engineering stress–strain curve is still widely used and

a number of properties are derived from it. Figure 2.6 shows the engineering stress strain curve

calculated from the load, extension diagram

Engineering stress can be calculated by this equation

0A

Feng (2.3)

And engineering strain as

%1000

lleeng (2.4)

In Figure 2., the initial yield stress is

0

0)(AFy

f (2.5)

The maximum of engineering stress is called tensile strength and calculated as

0

max

APTS (2.6)

maxF

yF

maxl

8

Figure 2.6 Engineer stress-strain curve (Marciniak, Z.et al. 2002).

The maximum uniform elongation, uE , is the elongation at maximum load at

maximum load as the cross-sectional area is no longer 0A .

If the strain scale near the origin is greatly increased, the elastic part of the curve

would be seen, as shown in Figure 2.7. The strain at initial yield, ye , is very small, typically

about 0.1%. The slope of the elastic part of the curve is the elastic modulus, also called Young’s

modulus:

Figure 2.7 The elastic behavior of typical tensile test (Marciniak, Z.et al. 2002).

In some materials, the transition from elastic to plastic deformation is not sharp

and it is difficult to establish an accurate yield stress. This is the stress to produce a specified

small plastic strain 0.2%, i.e. the elastic strain at yield. Proof stress is determined by drawing a

9

line parallel to the elastic loading line which is offset by the specified amount, as shown in Figure

2.8.

Figure 2.8 Diagram used to determine the proof stress in a material (Marciniak, Z.et al. 2002).

2.2.5 Anisotropy

In the principles of Anisotropy properties of the material is not equal in all

directions. Therefore the values of r necessary to average in each direction (0o, 45o, 90o) as

shown in Figure 2.9 and the r value in each direction will be average to use.

4

2 90450 RRRR (2.7)

Figure 2.9 Measurement of r value by tensile specimen from three directions (ASTM, 1998).

10

2.3 Tubular blank

Tubing and Pipe are considered to be separate products, although geometrically they are

quite similar. ‘‘Tubular products’’ infers cylindrical products which are hollow, and the

classification of ‘‘pipe’’ or ‘‘tube’’ is determined by the end use. ASTM and the American

Petroleum Institute (API) provide specifications for the many categories of pipe according to the

end use. Other classifications within the end use categorization refer to the method of

manufacture of the pipe or tube, such as seamless, cast, and electric resistance welded. Pipe and

tube designations may also indicate the method of final finishing, such as hot finished and cold

finished.

Structural tubing is used for general structural purposes related to the construction

industry. ASTM provides specifications for this type of tubing. Mechanical tubing is produced

to meet particular dimensional, chemical, and mechanical property and finish specifications

which are a function of the end use, such as machinery and automotive parts. This category of

tubing is available in welded (ERW) and seamless form.

In the electric resistance-welded (ERW) pipe process (Figure 2.10), upon exiting the

forming mill, the longitudinal edges of the cylinder formed are welded by flash-welding, low-

frequency resistance-welding, high-frequency induction-welding, or high-frequency resistance-

welding. All processes begin with the forming of the cylinder with the longitudinal seam butt

edges ready to be welded.

Figure 2.10 Electric resistance welded pipe process. (PIPING HANDBOOK, 2000)

Progressive strip

cross section

Flat steel strip Flat steel strip

Forming rolls

Pressure roll

Welded tube

Welding electrode

11

It is important to select the optimum tube material for hydroforming in order to achieve

successful THF. In this study focus on electric resistance welding (ERW) tube (Figure 2.11)

commonly used in Thai industry, a common carbon steel tubing commonly grade STKM 11A,

with 28.6 mm outer diameter and 1.2 mm thick is studied

Figure 2.11 Electric Resistance Welding (ERW) Tube

2.4 Strain-based forming limit curve

The concept of a forming limit for sheet metal alloys was pioneered by Keeler and

Backofen (1963) and Goodwin (1968). They experimentally determined forming limits by

measuring the principal surface strains on sheet specimens formed to the onset of localized

necking. Keeler and Goodwin also generated forming limit diagrams (FLD) in principal strain

space in which a forming limit curve (FLC) represents the boundary beyond which there is a risk

of necking for a given sheet metal. Therefore, combinations of principal surface strains that place

below the FLC lead to a safe forming operation, whereas those that place above it lead to failure

(Muammer Koç, 2008). Figure 2.12 represents a typical FLD for has three basic zones-red,

yellow, and green. Any points plotting in the red zone indicate that the part have failed. Visible

defects such as split necks fall in the red zone.

Electric Resistance Welding

line

12

Figure 2.12 Three basic zones - red, yellow, and green of Forming limit diagram.

Circular grids are electrochemically etched onto the surface of sheet steel samples. After

the tests, Dimensions of the grid circles at the pole will be measured to calculate true major and

minor strains by Equations (2.8)-(2.9), Figure 2.13. The critical major and minor strains are

plotted to construct the forming limit curve (FLC) for sheet steel material.

Figure 2.13 FLD with different principle strain ratio

ε = ln (2.8)

ε = ln (2.9)

ξ = -1 ξ = -0.5 ξ = 0 ξ = 1

Min

or st

rain

( 𝜀)

Minor strain (𝜀 )

Forming Limit Curve

Savety Curve

13

Since many tubes used for hydroforming applications are roll-formed from rolled sheet, it

was argued that the concept of the FLD (i.e. from sheet steel) equally applies to tubes. There are

important reasons why the standard FLC is not generally applicable to tubular hydroformed parts.

One of them being the fact that the roll – forming process of a sheet steel into a tube will incur pre

– strained conditions onto the fresh tube. This is known to affect FLC even in the steel sheet

forming

The forming limit diagram (FLD) of tubular materials should be established, because it

directly influences the formability of the hydraulic forming processes. A few studies concerning

the loading paths or the forming limit of tubes and sheets have been reported. For example,

Yeong-Maw Hwang (2008) uses bulge tests to establish the forming limit diagram (FLD) of

tubular material AA6011 are compared with the forming limits from the analytical FLCs using

the n values obtained by tensile tests and bulge tests. Nefussi and Combescure (2002) used

Swift’s criteria for sheets and tubes and took into account the buckling induced by axial loading

in order to predict plastic instability for tube hydroforming. Korkolis and Kyriakides (2008)

studied anisotropic aluminum tubes (Al-6260-T4 tubes) for hydroforming applications. Then

investigated the performance of Hosford and Karafillis-Boyce non-quadratic anisotropic yield

functions in predicting the response and bursting of tubes loaded under combined internal

pressure and axial load. Comparison between numerical simulations and hydroforming

experiments on aluminum tubes have indicated that localized wall thinning and burst can be very

sensitive to the constitutive description employed for the material. Tirosh et al. (1996) explored

an optimized loading path for maximizing the bulge strain between necking and buckling

experimentally with aluminum A5052 tubes. Xing and Makinouchi (2001) investigated the

differences in forming limits of tubes under internal pressure, independent axial load or torque

based on Yamada’s plastic instability criteria and Hill’s quadratic yield function. The above

theory coupled with an in-house finite element code ITAS3d was used to control the material

flow and to prevent the final failure modes from occurring. They concluded that the two Swift’s

criteria are applicable to predict necking and that a special attention has to be paid to plastic

buckling, because the critical strains corresponding to buckling are much smaller than the critical

strains predicted by the necking criteria. However, experiments are required to validate their

theoretical results. So far, a consistent conclusion for forming limit theorems of tubular materials

has not been established and the forming limit diagram for STKM 11A tubes has not been found.

14

In this study, hydraulic forming apparatus are developed. Experiments of bulge tests

with and without axial feeding are accomplished. Loading paths, which correspond to the strain

paths with constant strain ratios at the pole of the forming tube, are determined by “LS-DYNA”

software and result are the internal pressure and axial feeding are used to control the forming

apparatus in the forming limit experiments. The experimentally obtained forming limits are

compared with analytically obtained FLCs using Finite Element software.

2.4.1 Formulation of plastic instability criteria

Swift’s diffused necking criterion (Swift, 1952) for thin sheets and Hill’s

localized necking criterion (Hill, 1952) associated with the Hill’s non-quadratic yield function

(Hill, 1979) are used to construct the FLC for the bi-axial tensile strain zone and tensile–

compressive strain zone, respectively. The subtangents of the stress–strain curve, Zd, and Zl, as

diffused necking and localized necking occur, respectively, are given as below,

= (2.10)

= (2.11)

𝑍 = ( ⁄ ) ( ⁄ )( ⁄ ) ( ⁄ ) (2.12)

𝑍 = ⁄( ⁄ ) ( ⁄ ) (2.13)

Where 𝜎 and 𝜀 are the effective stress and effective strain, respectively. g is the plastic potential

function. The physical meaning of subtangents Zd and Zl is shown in Figure 2.14. It is clear that

Z increases as the strain at necking increases. For the detailed derivation of Zd and Zl, please refer

to appendixes A1 and A2.

15

Figure 2.14 Schematic figure of the subtangent of a stress strain curve as necking occurs.

(Yeong-Maw Hwang. 2009)

For consideration of the effects of normal anisotropy of the material, the Hill’s non-

quadratic yield function (Hill, 1979) is used to derive the critical strains for diffused necking and

localized necking. At first, let the plastic potential function equal the Hill’s non-quadratic yield

function with a plane stress state:

g = 𝜎 = ( ) [(1 + 2𝑟)|𝜎 − 𝜎 | + |𝜎 + 𝜎 | ] (2.14)

where m is the exponent of the yield function and r the normal anisotropy of the material. Then,

substituting Equation (2.14) into Equation (2.12) and (2.13), the subtangents for diffused necking

and localized necking, respectively, are expressed as

Zd=[2(1+r)]1 m⁄ (1+2r) 1-α 1-αm-1+(1+α)|1+α|m-1

(1+α) (1+2r)2 1-α2m-2 |1+α|2m-2 +2(1+2r) 1-α 1-α2

m-1

× [(1 + 2𝑟)|1 − 𝛼| + |1 + 𝛼| ]( )⁄ (2.15)

Zl=[2(1+r)]1 m⁄ (1+2r) 1-α

m+|1+α|m

m-1 m⁄

2|1+α|m-1 (2.16)

where α is the principal stress ratio (𝛼 = 𝜎 /𝜎 )

Let the effective stress of the material be expressed by a power law of its equivalent strain:

𝜎 = 𝐾𝜀 (2.17)

16

where K and n are the strength coefficient and strain-hardening exponent, respectively, of the

material. Substituting Equation (2.17) into Equation (2.10) and (2.11), the critical effective strains

for diffused necking and localized necking can be obtained respectively as

𝜀 = 𝑛𝑍 , 𝜀 = 𝑛𝑍 (2.18)

From the flow rule (Chen and Han, 1995),

𝑑𝜀 = 𝑑𝜆 = ( ) [(1 + 2𝑟)|𝜎 − 𝜎 | + |𝜎 + 𝜎 | ]𝑑𝜆 (2.19)

𝑑𝜀 = 𝑑𝜆 = ( ) [−(1 + 2𝑟)|𝜎 − 𝜎 | + |𝜎 + 𝜎 | ]𝑑𝜆 (2.20)

where dλ is a positive scalar factor of proportionality. The principal strain increment ratio can be

obtained as

𝜉 = = ( )| | | |( )| | | | (2.21)

After arrangement of the above equation, the stress ratio can be obtained as

α= [(1+2r)|1+ξ|]1 m-1⁄ - 1-ξ 1 m-1⁄

[(1+2r)|1+ξ|]1 m-1⁄ + 1-ξ 1 m-1⁄ (2.22)

From the plastic work increment W = σ dε = σdε , it follows that

𝑑𝜀̅ = = [ ( )] ⁄ ( )/( ) ( )

( )⁄ (2.23)

After combining with Equations (2.19) and (2.20), the major principal strain increment can be

expressed as a function of the effective strain increment as below.

𝑑𝜀 = [ ( )] / ×| | ( )⁄ ( ⁄ ) ( )⁄ | | ( )⁄ ( )⁄ (2.24)

17

During the forming process the stress ratio α is assumed to be constant; accordingly, the strain

increment ratio, 𝜉, equal to the strain ratio is a constant. The forming limit for the major principal

strain 𝜀 can be obtained by integration on both sides of Eq. (2.24), as given below:

ε = [ ( )] ⁄ ×| | ( )⁄ ( ⁄ ) ( )⁄ | | ( )⁄ ( )⁄

= [ ( )] ⁄ ×| | ( )⁄ ( ⁄ ) ( )⁄ | | ( )⁄ ( )⁄ (2.25)

Where Z is equal to Zd and Zl, as given in Equations (2.15) and (2.16), for diffused necking and

localized necking, respectively. The critical minor principal strain can be obtained from ε2C=ξ ε1C . A flow chart for determining the forming limit strains is shown in Figure 2.15. At first, the

exponent of the yield function, m, the strain-hardening exponent, n, and the normal anisotropy, r,

of the material are input. After the strain ratio ξ is given, the stress ratio can be calculated by

Equation (2.22). If, ξ > 0 diffused necking criterion is used. Otherwise, localized necking criterion

is used. The critical major strains corresponding to different obtained critical strain pairs (ε2C, ε1C) for 1 > ξ >-0.5

18

Start

Input n, r, m values

Set strain ratio ξ=-0.5

ξ≥0

Calculate ZdUsing Eq.(6)

Calculate ZlUsing Eq.(7)

Calculate ε1c Using Eq.(16)

ε2c = ξ ε1c

ξ≥1

Plot FLC

Stop

ξ = ξ +0.1

Yes

No

Yes

No

Figure 2.15 Flow chart for determining the critical major and minor principal strains.

Figure 2.16(a) and (b) shows the forming limit curve and the yield locus, respectively,

using Hill’s non-quadratic yield function with r = 1.856 and n = 0.226. The region for stress ratios

(𝛼 = 𝜎 𝜎⁄ ) from 0.5 to 0 in the yield locus figure corresponds to that for strain ratios (𝜉 =𝜀 𝜀⁄ ) from 0 to -0.5 in FLC figure.

19

(a) Forming limit curve

(b) Yield locus

Figure 2.16 The forming limit curve and yield locus with Hill’s non-quadratic yield function.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

𝜎 /𝜎

-1 1

1

-1

0.5

-0.5

0.5 -0.5

Min

or st

rain

( 𝜀)


𝜎 /𝜎

20

2.4.2 FLC obtained by Finite Element software: DYNAFORM

FE simulations (Dynaform) are used to determine the loading paths in this study.

The analytical FLCs using the n and r values obtained by tensile tests. The FLC curve

approximately according to Keeler’s formula as given below:

𝐹𝐿𝐷 = ( . . ) , 0 < 𝑡 < 2.54 𝑚𝑚 ; (2.26)

𝐹𝐿𝐷 = [ ( . . ) ] , 2.54 ≤ 𝑡 ≤ 5.33 𝑚𝑚 ; (2.27)

The shape of FLC is determined by the formulas below:

𝜀 = 𝐹𝐿𝐷 + 𝜀 (0.027254𝜀 − 1.1965) 𝜀 < 0 (2.28)

𝜀 = 𝐹𝐿𝐷 + 𝜀 (−0.008565𝜀 − 0.784854) 𝜀 < 0 (2.29)

The critical major and minor strains are calculated Keeler’s formula and plotted

to construct the forming limit curve (FLC), as show in Figure 2.17.

Figure 2.17 The forming limit curve with Keeler’s formula.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

Min

or st

rain

( 𝜀)


21

2.5 Ductile fracture criterion

A metal that plastically deforms extensively without the onset of fracture is normally

termed as ductile. Ductile fracture occurs when a material is subjected to large deformation. In a

metal forming process, the ductile fracture is so complicated that many experimental

investigations as well as theoretical predictions have been performed to determine that of the

metal, and various criteria have been proposed to evaluate the forming limit (Cockroft M. 1968,

Norris DM. 1978, Brozzo P. 1972, McClintock FA. 1968, Oyane M. 1980). Unfortunately, it

appears that the various criteria have a number of validity restrictions and there are no universal

criteria for metal forming process. It is well known that the forming limit of hydroforming

process depends greatly upon the deformation history. Therefore, the histories of stress and strain

may have to be considered in the criteria. Among these criteria, the ductile fracture criterion

proposed by Oyane (1980) was successfully introduced in prediction of forming limit of a sheet

metal forming process by Takuda and others (Takuda H. 1999, Takuda H. 1999, Mori K. 1996,

Takuda H. 2000). The past researches show that Oyane’s ductile fracture criterion can be applied

to evaluate the forming limit in a wide range of metal forming processes, including aluminum

alloy material which does not have evident localized necking before fracture. Oyane’s ductile

fracture criterion assumes that the history of hydrostatic stress affects the occurrence of the

ductile fracture;

∫ + 𝐶 𝑑𝜀̅ = 𝐶 (2.30)

where 𝜀̅ is the equivalent strain at fracture, 𝜎 the mean stress, 𝜎 the equivalent stress, 𝜀 ̅the

equivalent strain, and 𝐶 , 𝐶 the material constants. In Equation (2.30), it is represented that the

fracture occurs when the value of the left-hand side reaches that of the right-hand side. Oyane’s

criterion requires two material constants 𝐶 and 𝐶 , which can be obtained from limit strains

corresponding to uniaxial tensile test and plane-strain tensile test.

Equation (2.30) can be rewritten as follows:

𝐼 = ∫ + 𝐶 𝑑𝜀 ̅ (2.31)

The histories of stress and strain in each element during forming are calculated by the FEM, and

22

the ductile fracture integral I in Equation (2.31) is obtained for each element. When the integral

value I of Equation (2.31) reaches 1.0, the fracture will occur. This ductile fracture value I can be

calculated for every finite element during the forming process.

Figure 2.18 Forming limit diagram obtained experimentally for a STKM-11A tube

(Li-Ping Lei, 2002).

Figure 2.18 shows the experimentally obtained forming limit diagram from bulge test of a

STKM-11A tube (Li-Ping Lei, 2002). The black dots indicate the strains just at the fracture site.

Namely, the ultimate strains for fracture are distributed in the figure. After the localized necking

occurs, the plastic deformation almost ceases outside of the necking, while the deformation at the

necking region progresses under plane-strain condition to fracture. It is found that the strains after

the localized necking tend to decrease with increase in the strain ratio, 𝛽 = 𝜀 /𝜀 , where 𝜀 and

𝜀 are the major and the minor strains on the tube. As a result, the solid circles are linearly

distributed as shown in Figure 2.18.

According to the Mises yield criterion and the Levy–Mises stress–strain increment

relationship, the terms in Equation (2.30) are expressed by the strain ratio, 𝛽, as

= ( ) = 𝐴(𝛽), (2.32)

𝑑𝜀̅ = (1 + 𝛽 + 𝛽 )𝑑𝜀 = 𝐵(𝛽)𝑑𝜀 (2.33)

Min

or st

rain

( 𝜀)


23

Figure 2.19 depicts the above relations. The rations 𝜎 𝜎⁄ and 𝑑𝜀̅ 𝑑𝜀⁄ increase with 𝛽.

Since the unknowns are two material constants 𝐶 and𝐶 , two arbitrary fracture

strains𝜀 (𝛽 ),𝜀 (𝛽 ) in Figure 2.18 should be chosen to get these values. Provided that the

strain ratios (𝛽) are constant during the deformation until the fracture initiation, the material

constants are simply calculated from Equation (30), (32) and (33) as the following:

𝐵(𝛽 )𝜀 (𝛽 ) −1𝐵(𝛽 )𝜀 (𝛽 ) −1

𝐶𝐶 = −𝐴(𝛽 )𝐵(𝛽 )𝜀 (𝛽 )

−𝐴(𝛽 )𝐵(𝛽 )𝜀 (𝛽 ) (2.34)

Figure 2.19 Variations of 𝜎 𝜎⁄ and 𝑑𝜀̅ 𝑑𝜀⁄ with respect to strain ratio 𝛽 (Li-Ping Lei, 2002).

Figure 2.20 Determination of C1 and C2 for a STKM-11A tube (Li-Ping Lei, 2002).

Min

or st

rain

( 𝜀)


24

The material constants C1 and C2 are determined approximately so that the fracture

strains calculated for constant ratios 2t the experimental ones as appeared in Figure 2.20 and then

C1 =-0.069, C2 =0.255 for STKM-11A material are obtained. The calculated fracture strains are

distributed linearly for each pair of material constants. Hence it is found that the distributions of

the fracture strains calculated from the ductile fracture criterion are similar to those of the black

dots as shown in Figure 2.20.

2.6 Effect of non-linearity of strain path.

Several researchers have shown experimentally that a non-linear strain path can change

the shape and location of the FLC in strain space. Ghosh and Laukonis (1976) investigated sheet

metal forming limit curve based on plastic deformation energy by prestraining stainless steel

specimens to various levels of strain and in different deformation. Graf and Hosford (1993a,

1993b) also reported strain-path effects for 2008 T4 aluminium pre-strained in uniaxial, equi-

biaxial and near plane-strain tension. The result was a different FLD for each value of prestrain as

shown in Figure 2.21. Graf and Hosford (1993a) also attempted to predict the shifted FLD using

the Marciniak-Kuczynski (M-K) analysis; however, the predicted FLC did not correlate well with

experimental data when the prestrain was in equi-biaxial tension.

Figure 2.21 Influence of strain path on the FLC (adapted from Graf and Hosford, 1993).

25

These experimental observations show that, depending on the loading history, the actual

FLC can be significantly different from the as-received FLC. As a result of a change in shape and

position, combinations of principal strains that are safe from necking can lie above the as-

received FLC, and conversely, failures can take place at strains below the as-received FLC.

Furthermore, during any forming operation, different locations on a part undergo different strains

and forming modes. If the component is manufactured in two or more forming stages, the overall

strain path in each location can be severely non-linear as a result of following one strain path in

one forming stage and a different strain path in the next forming stage. In order to obtain a

standardized assessment of the forming limit curve, the strain path of the bulged sample has to be

controlled as linear as possible (i.e., constant strain ratio). This would call for one and the same

material to evaluate the forming severity of parts that were produced in complex, multi-stage

forming processes such as are typical for hydroformed tubular components.

CHAPTER 3

RESEARCH METHODOLOGY

This research aimed to establish the forming limit curve (FLC) of tubular material low

carbon steels commonly used in Thai industry, namely STKM 11A with 1.2 mm thickness and

28.6 mm outer diameter, compare these experimentally obtained FLCs against analytical and

empirical ones available in FEA software (Dynaform) and Formulation of plastic instability

criteria, and verify these FLCs with real part hydroforming experiments. First, bulge forming

apparatus of fixed bulge length and a hydraulic test machine with axial feeding were used to carry

out the bulge tests that were able to keep linear strain part at the apex of the bulging tube. FEM

was used to determine die proper insert parameters such as free bulge length (L), die entry radius

(rd). Second, loading paths corresponding to the strain paths with constant strain ratios at the apex

of the bulging tube were also determined by FE simulations, which in turn were used to control

the internal pressure and axial feeding punch of the test machine. Third, preparing the tube blank,

circular grids were electro chemically etched onto the surface of tube samples. Then, after

running bulge tests, the major and minor strains of the grids beside the bursting line on the tube

surface are measured to construct the forming limit curve. Finally, compare these FLCs against

empirical FLCs and verify these FLCs with real part forming experiments to achieve the

objectives and scope of this research. The procedure of research is as follows.

1. Study tools and equipment used in research.

2. Study material properties used in the experiments.

3. Study the forming process.

4. Learn how to use Dynaform.

5. Run Tube Hydroforming simulations for test die insert design and process parameter

determination.

6. Prepare Tube blank such as cutting, sanding, griding of any sharp edges and electro

chemically etched onto the surface of tube samples.

7. Conduct the experiment, collect and analyze the data.

8. Construct the forming limit curve.

9. Compare and verify the obtained FLD’s.

27

3.1 Numerical Investigation

3.1.1 Test die insert design

Several researchers (Jieshi Chen, Xianbin Zhou and Jun Chen, 2009) have

shown experimentally that non-linear strain path can change the shape and location of the FLC.

Nevertheless, to an extent, this effect on the FLC can be minor if the non - linearity is kept small.

In order to obtain a standardized assessment of the forming limit curve, the strain path at the apex

of the bulged sample has to be controlled as linear as possible (i.e., constant strain ratio). In this

work, it was necessary to design proper testing die insert geometry – 1)die entry radius(rd) and 2)

bulge length(L), as show in Figure 3.1.

Figure 3.1 Schematic diagram of the test die insert parameters

An FEA software (DYNAFORM) was used to conduct all the simulations in this

work. Due to its symmetry, only one half of the testing a die insert and tube sample were model,

see Figure 3.2. In each case of simulation run, several process parameters (i.e. pressure and axial

Free bulge length (L)

Initial tube blank

Outer diameter (OD)

Initial tube thickness (t)

Axial Punch

Die entry radius (rd)

Axial feed Axial feed

Pressurized water inlet

Pressure

28

feed distance) were tried in an attempt to form the sample with linear strain paths. Any elements

in the red indicate that the parts have failed.

Figure 3.2 The formed part show in half model

The specimen tubes were modeled with 1 mm thickness and 25.4 mm outer

diameter. Two geometry parameters were used to investigate, namely 1) L/OD and 2) rd/t, see

table 3.1. A series of simulation were conducted with various die insert geometry and tube

sample dimensions, see table 3.2, to determine the proper testing die insert geometer.

Table 3.1 Design of simulation matrix

L/OD 1 2 3

L 25.4 50.8 76.2

OD 25.4 25.4 25.4

rd/t 5 15 25

rd 5 15 25

t 1 1 1

𝑟

𝑡 2

29

Table 3.2 A series of simulation

Model L/OD rd/t L OD rd t

RUN01 1 5 25.4 25.4 5 1

RUN02 1 15 25.4 25.4 15 1

RUN03 1 25 25.4 25.4 25 1

RUN04 2 5 50.8 25.4 5 1

RUN05 2 15 50.8 25.4 15 1

RUN06 2 25 50.8 25.4 25 1

RUN07 3 5 76.2 25.4 5 1

RUN08 3 15 76.2 25.4 15 1

RUN09 3 25 76.2 25.4 25 1

It was found that only properly designed die insert geometry relative to tube

sample geometry – 1) tube outer diameter (OD) and 2) tube sample thickness (t) will allow the

linear strain path during testing. Four strain ratios (𝜉 = 𝜀 𝜀⁄ ) -0.1, -0.2, -0.3 and -0.4 were the

slopes of each strain path under investigation in this work. It no possible internal pressure and

axial feed distance were found to fulfill the constant strain ratios then it was concluded that the

specific die insert geometry is not proper.

Table 3.3 Simulation results

Model L/OD rd/t L(mm) OD(mm) rd(mm) t(mm) Resultant strain ratio(𝜉)

RUN01 1 5 25.4 25.4 5 1 Non-linear

RUN02 1 15 25.4 25.4 15 1 Linear

RUN03 1 25 25.4 25.4 25 1 Non-linear

RUN04 2 5 50.8 25.4 5 1 Non-linear

RUN05 2 15 50.8 25.4 15 1 Non-linear

RUN06 2 25 50.8 25.4 25 1 Non-linear

RUN07 3 5 76.2 25.4 5 1 Non-linear

RUN08 3 15 76.2 25.4 15 1 Non-linear

RUN09 3 25 76.2 25.4 25 1 Non-linear

30

Table 3.3 summarizes the results of this simulation finding. Only die insert

geometry in simulation RUN02 yields the satisfying linear strain path requirement (i.e. constant

strain ratio𝜉 ± 0.01). It can be seen that only RUN02 is able to keep the strain ratio of -0.4

constant (i.e. linear) all the way to the fracture limit, FLC.

The ratio of Model Run02 (L/OD=1 and rd/t=15), were put to test in another

outer diameter and thickness of tube sample. A series of simulation were conducted with two

geometry ratio to verify, namely 1) L/OD=1 and 2) rd/t=15, see table 3.4, to verify the proper

testing die insert geometer.

Table 3.4 A series of simulation, L/OD=1 and rd/t=15

Model L/OD=1 rd/t=15

L(mm) OD(mm) rd(mm) t(mm)

TEST01 12.7 12.7 7.5 0.5

TEST02 12.7 12.7 15 1

TEST03 12.7 12.7 30 2

TEST04 25.4 25.4 7.5 0.5

TEST05 25.4 25.4 15 1

TEST06 25.4 25.4 30 2

TEST07 50.8 50.8 7.5 0.5

TEST08 50.8 50.8 15 1

TEST09 50.8 50.8 30 2

Table 3.5 summarizes the results of second simulation finding. Die insert

geometry in simulation TEST01, TEST05 and TEST09 yields the satisfying linear strain path

requirement (i.e. constant strain ratio𝜉 ± 0.01). It was found the tool geometry that can keep the

strain ratio constant is not dependent on the thickness but dependent on only OD of the tube, as

given in Equations (3.1)-(3.2), see figure 3.3.

31

Table 3.5 Result of Simulation, L/OD=1 and rd/t=15

Model L/OD=1 rd/t=15 Results

L(mm) OD(mm) rd(mm) t(mm)

TEST01 12.7 12.7 7.5 0.5 Linear

TEST02 12.7 12.7 15 1 Non-linear


TEST04 25.4 25.4 7.5 0.5 Non-linear

TEST05 25.4 25.4 15 1 Linear


TEST07 50.8 50.8 7.5 0.5 Non-linear


TEST09 50.8 50.8 30 2 Linear

𝐿 = 𝑂𝐷 (3.1)

𝑟 = ×. (3.2)

Figure 3.3 testing die insert geometry

3.1.2 Determination of loading paths by FE-simulations

The ratio of Proper Model according to equations (3.1) and (3.2), were put to

model with 1.2 mm thickness and 28.6 mm outer diameter tube blank. Internal pressure and axial

feed distance under investigation in this work were used to control the four strain ratios (𝜉 =𝜀 𝜀⁄ ) -0.1, -0.2, -0.3 and -0.4 at the apex of the bulged sample as linear as possible. The

corresponding loading paths to the four linear strain paths are determined by FE simulations,

shown in Figure 3.4, 3.5 and 3.6. Results of the formed simulation with four different strain ratios

Outer diameter (OD)

𝑟 = 15 × 𝑂𝐷25.4

𝐿 = 𝑂𝐷

32

(𝜉 = 𝜀 𝜀⁄ ) -0.1, -0.2, -0.3, -0.4 and no feeding show in half model, see Figure 3.7 and each of

strain path are shown in Figure 3.8.

Feeding Distance 𝛏=-0.1 𝛏=-0.2 𝛏=-0.3 𝛏=-0.4

0 0 0 0 0 1 0.001176 0.002941 0.011765 0.023529 2 0.002353 0.005882 0.023529 0.047059 3 0.003529 0.008824 0.035294 0.070588 4 0.004706 0.011765 0.047059 0.094118 5 0.005882 0.014706 0.058824 0.117647 6 0.007059 0.017647 0.070588 0.141176 7 0.008235 0.020588 0.082353 0.164706 8 0.009412 0.023529 0.094118 0.188235 9 0.010588 0.026471 0.105882 0.211765 10 0.011765 0.029412 0.117647 0.235294 11 0.012941 0.032353 0.129412 0.258824 12 0.014118 0.035294 0.141176 0.282353 13 0.015294 0.038235 0.152941 0.305882 14 0.016471 0.041176 0.164706 0.329412 15 0.017647 0.044118 0.176471 0.352941 16 0.018824 0.047059 0.188235 0.376471 17 0.02 0.05 0.2 0.4 18 0.03 0.08 0.3 0.8 19 0.07 0.15 0.4 1.3 20 1.25 2.5 4.75 9

Figure 3.4 Feeding distance (mm) with time(s)

0

1

2

3

4

5

6

7

8

9

0 5 10 15 20

𝛏=-0.1

𝛏=-0.2

𝛏=-0.3

𝛏=-0.4

Feed

ing

dista

nce

(mm

)

Times(s)

33

Time(s) Internal Pressure (bar) 𝛏=-0.1 𝛏=-0.2 𝛏=-0.3 𝛏=-0.4 No

feeding 0 0 0 0 0 0.000 1 220 220 220 220 13.325 2 221.7737 221.3553 220.8421 220.1579 26.650 3 223.5474 222.7105 221.6842 220.3158 39.975 4 225.3211 224.0658 222.5263 220.4737 53.300 5 227.0947 225.4211 223.3684 220.6316 66.625 6 228.8684 226.7763 224.2105 220.7895 79.950 7 230.6421 228.1316 225.0526 220.9474 93.275 8 232.4158 229.4868 225.8947 221.1053 106.600 9 234.1895 230.8421 226.7368 221.2632 119.925

10 235.9632 232.1974 227.5789 221.4211 133.250 11 237.7368 233.5526 228.4211 221.5789 146.575 12 239.5105 234.9079 229.2632 221.7368 159.900 13 241.2842 236.2632 230.1053 221.8947 173.225 14 243.0579 237.6184 230.9474 222.0526 186.550 15 244.8316 238.9737 231.7895 222.2105 199.875 16 246.6053 240.3289 232.6316 222.3684 213.200 17 248.3789 241.6842 233.4737 222.5263 226.525 18 250.1526 243.0395 234.3158 222.6842 239.850 19 251.9263 244.3947 235.1579 222.8421 253.175 20 253.7 245.75 236 223 266.5

Figure 3.5 Internal Pressure (bar) with time (s)

0

50

100

150

200

250

300

0 5 10 15 20

𝛏=-0.1

𝛏=-0.2

𝛏=-0.3

𝛏=-0.4

No feeding

Inte

rnal

Pre

ssur

e (b

ar)

Times(s)

34

Figure 3.6 Feeding distance (mm) with Internal Pressure (bar)

Figure 3.7 a.) No feeding

Figure 3.7 b.) 𝜉(𝜀 𝜀 ) = −0.1⁄

0

50

100

150

200

250

300

0 2 4 6 8 10

𝛏=-0.1 𝛏=-0.2 𝛏=-0.3 𝛏=-0.4 In

tern

al P

ress

ure

(bar

)

Feeding distance (mm)

35

Figure 3.7 c.) 𝜉(𝜀 𝜀 ) = −0.2⁄

Figure 3.7 d.) 𝜉(𝜀 𝜀 ) = −0.3⁄

Figure 3.7 e.) 𝜉(𝜀 𝜀 ) = −0.4⁄

Figure 3.7 Simulation results with four strain ratios (𝜉 = 𝜀 𝜀⁄ ) -0.1, -0.2, -0.3, -0.4 and no

feeding

36

Figure 3.8 Different strain paths investigated

3.2 Experimental Investigation

3.2.1 FLC testing apparatus

A bulge test apparatus with a fixed bulge length without axial feeding as shown

in Figure 3.9 is used to implement the forming limit experiments to obtain the strain path on right

side of the FLD. The specimen 300 mm initial tube lengths are expanded at both the end of the

tube and fixed by punches during forming.

Figure 3.9 The experimental apparatus for bulge tests without axial feeding.

ξ=-‐0.1

Maj

or st

rain

( 𝜀)


ξ=-‐0.2 ξ=-‐0.3

ξ=-‐0.4

No feeding No feeding No feeding

1.00

0.80

0.60

0.40

0.20

0.00 -0.1 -0.5 -0.3 -0.1 -0.3 -0.5

37

A hydroforming test machine with axial feeding is used to conduct the

experiments with 200 mm initial tube length to obtain the strain paths on the left side of

the FLD, in which tensile and compressive strains occur as shown in Figure 3.10

Figure 3.10 The experimental apparatus for bulge tests with axial feeding.

Figure 3.11 Schematic diagram of the experimental apparatus for bulge tests

3.2.2 THF Test Specimens

Before bulge tests, the tubes of STKM low carbon steels are 200 mm (with axial

feeding) and 300 mm (without axial feeding) long, 1.2 mm thick, and 25.8 mm in outer diameter.

They are rounded off of any sharp edges in the tubular blanks by lathe machine, for the tubes used

for the forming limit experiments, circular grids with a diameter of 2.5mm as shown in Figure

3.12 are electrochemically etched on the tube surface before the experiments, see Figure 3.12.

38

Figure 3.11 Circular grids with a diameter of 2.5mm

Figure 3.12 THF Test Specimens

3.2.3 Hydraulic Press

In the hydroforming process, hydraulic presses are typically used to open and

close the die and to provide enough clamping load during the forming period to prevent die

separation. A 200 ton hydraulic press was used in this experiment. The press is controlled by a

CNC controller shown in Figure 3.13.

Figure 3.13 Hydraulic press and CNC controller

39

3.2.4 Pressure system, Hydraulic cylinders and punches

The pressure system (pump, intensifier and control and relief valves, coolers,

etc.) provide the required pressure levels, which are controlled by CNC controller, shown in

figure 3.14. The axial punches are necessary to seal the end of the tube to avoid pressure losses

and to feed material into expansion regions. They should feed the material in a controlled path,

and in synchronization with internal pressure.

Figure 3.14 CNC controller used to control internal pressure and axial punches

3.3 Grid measurement

After bulge tests, Dimensions of the grid circles at the pole (-45˚ to 45˚from welding

line) were accurately measured to obtain true major and minor strains by Equations. (2.8)- (2.9).

The critical major and minor strains are plotted to construct the forming limit curve (FLC) for

tubular material.

3.3.1 Digital Microscope

A Digital Microscope that shown in Figure 3.15.is used to take snapshots of the

deformed grids, which are later measured for true major and minor strains. After the bulge tests,

the measured major and minor strains on the tube surface are used to construct the forming limit

curve. A grid is captured by Dino Capture Software and measure the diameter of deformed grids

as show in Figure 3.16

Figure 3.15 Digital Microscope (Dino-Lite)

40

Figure 3.16 The deformed grids measured using Dino Capture Software

3.3.2 Grid Curvature

As specimen are tubular and final from are bulge shape, the captured grid from

Digital Microscope are projected from real deformed grids; therefore, corrective curve is

important to achieve the real deformed grid diameter and FLC. The curvature has two radii, 𝑟 is

meridian radius of curvature at the pole as shown in figure 3.17 and 𝑟 is circumferential radius

of curvature at the pole as shown in figure 3.18.meridian and circumferential radii of curvature at

the pole

Figure 3.17 𝑟 is meridian radius of curvature at the pole

Figure 3.18 𝑟 is circumferential radius of curvature at the pole

𝑙 ′

𝑟

𝑟

𝑙 ′

41

The digital camera with macro lens is used to capture the shape of bulge tube,

see in figure 3.19 and approximate the curve by CAD software, see in figure 3.20.

Figure 3.19 A photo of bulged tube for curvature measurement

Figure 3.20 Approximation of the curve by CAD software

Then, one can calculate the real deformed grid diameter by following equations.

𝑙 = 2𝑟 sin (3.1)

𝑙 = 2𝑟 sin (3.2)

Where 𝑙 = Major deformation

𝑙 = Minor deformation

𝑙 ′ = Captured major deformation

𝑙 ′ = Captured minor deformation

𝑟

𝑟

CHAPTER 4

EXPERIMENTATION AND RESULTS

This chapter explains experimentation and results of the experiments. A hydroforming test machine with axial feeding is designed for the left-hand side data in the forming limit diagram, in which tensile and compressive strains occur. Figure 4.1 shows a hydroforming test machine with axial feeding tooling set. A bulge test apparatus with a fixed bulge length without axial feeding as shown in Fig. 4.2 is used to implement the forming limit experiments to obtain the strain path on right side of the forming limit diagram. This test machine consists of three main parts for supporting the tooling; a hydraulic power system for providing the pressure source of the internal pressure and the feeding punches; and a control system.

Figure 4.1 Apparatus with feeding tooling set

Figure 4.2 Apparatus without feeding tooling set

43

4.1. Tube Hydraulic Bulge Test

A control system is used to control the forming pressure and the left and right axial feeding distances of the test machine according to the loading paths shown in Figure 4.3-4.4 and tryout in actual process.

Figure 4.3 Loading path, Feeding distance (mm) and Internal pressure (bar) with time(s)

Figure 4.4 Loading path, Feeding distance (mm) with Internal Pressure (bar)

0

50

100

150

200

250

300

0

1

2

3

4

5

6

7

8

9

0 5 10 15 20

Feeding distance 𝛏=-0.1




Pressure 𝛏=-0.1

Pressure 𝛏=-0.2

Pressure 𝛏=-0.3

Pressure 𝛏=-0.4

Pressure-No feeding

0

50

100

150

200

250

300

0 1 2 3 4 5 6 7 8 9 10

𝛏=-0.1 𝛏=-0.2 𝛏=-0.3 𝛏=-0.4

Feedi

ng di

stance

(mm)

Times(s)

Intern

al Pre

ssure

(bar)

Intern

al Pre

ssure

(bar)

Intern

al Pre

ssure

(bar)


44

4.1.1. Forming limit experiments with axial feeding

The actual responses of the forming pressures and axial feeding distances during the forming limit experiments are observed and recorded by computer PC-based data logger. Then, grouped correspond actual loading path specimen and separated off the non-corresponding actual loading path specimen. The actual responses are showed in Figure 4.6 and the results of the products after bulge tests with axial feeding for different strain ratios are shown in Figure 4.7. It is known that cracks or bursting lines occur around the pole of the bulged tubes and the maximum bulge height increases with the increase of the absolute value of the strain ratio

Figure 4.5 Loading path, Feeding distance (mm) with Internal Pressure (bar)

Figure 4.6 Results of the formed product for different strain paths.

0

50

100

150

200

250

300

350

0 2 4 6 8 10 12

Actual loading path-Set1Actual loading path-Set2Actual loading path-Set3Actual loading path-Set4

Intern

al Pre

ssure

(bar)


Set1 Set2 Set4 Set3

Set1 (1.66, 330.91) Set2 (3.33, 323.68)

Set3 (7.25, 308.04)

Set4 (9.57, 262.63)

45

In order to consider the strain path, several forming runs were conducted with the same loading path but were stopped at different deformed states. The set 1-4 loading paths of different deformed state are showed in Figure 4.7-4.10 respectively. First experiment, Feeding distance 1.66 mm is applied at the ends of tube and actual pressure up to 330 bars which is more than expandability of the welding seam; thus the tube burst at welding seam before localized necking occurred. Due to small feeding distance, it was hard to control the end feeding distance and corresponding pressure as results shown in Figure 4.7.

a.) loading path of the formed product of different deformed state-Set1

b.) Results of the formed product of different deformed state-Set1

Figure 4.7 loading path and Results of the formed product of different deformed state-Set1

0

50

100

150

200

250

300

350

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Set1-01Set1-02Set1-03Set1-04Set1-05Int

ernal

Pressu

re (ba

r)


Set1-01 (1.66, 330.91) Set1-02

(1.51, 308.65)

Set1-03 (1.23, 313.61)

Set1-04 (1.21, 271.77)

Set1-05 (0.38, 237.44)

Set1-01 Set1-02 Set1-04 Set1-03 Set1-05

46




0

50

100

150

200

250

300

350

0 0.5 1 1.5 2 2.5 3 3.5 4

Set2-01Set2-02Set2-03Set2-04Set2-05Set2-06

Intern

al Pre

ssure

(bar)



Set2-01 (3.33, 323.68)

Set2-03 (2.52, 323.67)

Set2-02 (2.74, 328.21)

Set2-04 (2.48, 327.48)

Set2-05 (2.28, 325.12)

Set2-06 (2.05, 323.91)

Set2-06

47



Figure 4.9 loading path and results of the formed product of different deformed state-Set3

0

50

100

150

200

250

300

350

0 1 2 3 4 5 6 7 8

Set3-01Set3-02Set3-03Set3-04Set3-05Set3-06Set3-07Set3-08Set3-09

Intern

al Pre

ssure

(bar)



Set3-01 (7.25, 308.04)

Set3-04 (4.64, 311.06) Set3-02 (4.94, 308.06) )

Set3-03 (4.67, 300.15) Set3-07

(3.36, 294.29)

Set3-06 Set3-08 Set3-07 Set3-09

Set3-05 (4.55, 311.00)

Set3-06 (4.33, 306.48)

Set3-08 (2.38, 277.90)

Set3-09 (2.34, 283.71)

48




0

50

100

150

200

250

300

350

0 2 4 6 8 10 12

Set4-01

Set4-02

Set4-03

Set4-04

Set4-05

Set4-06

Set4-07

Set4-08

Set4-09

Intern

al Pre

ssure

(bar)


Set4-01 Set4-02 Set4-04 Set4-03 Set4-05 Set4-06 Set4-08 Set4-07 Set4-09

Set4-01 (9.57, 262.63) Set4-04 (5.47, 266.62) Set4-02 (8.37, 263.13)

)

Set4-03 (7.75, 261.85) Set4-07 (4.24, 273.29)

Set4-05 (5.44, 264.94)

Set4-06 (4.40, 272.31)

Set4-08 (2.41, 267.37)

Set4-09 (1.96, 281.13)

49

4.1.2. Forming limit experiments without axial feeding

A bulge test apparatus with a fixed bulge length without axial feeding are installed for running experiment. The actual responses are showed in Figure 4.11 and corresponding specimen are showed in Figure 4.12 .

Figure 4.11 Loading path, Internal Pressure (bar) with times(s)

Figure 4.12 Results of the formed product without axial feeding. In order to consider the strain path, several forming runs were conducted with the same loading path but were stopped at different deformed states. The set 5 loading path of different deformed state are showed in Figure 4.13.

0

50

100

150

200

250

300

350

0 1 2 3 4 5 6 7 8 9 10

Actual loading path-Set5

Prescribed loading path-set5

Intern

al Pre

ssure

(bar)

Times(s)

50




0

50

100

150

200

250

300

350

400

0 2 4 6 8 10 12

Set5-01Set5-02Set5-03Set5-04Set5-05Int

ernal

Pressu

re (ba

r)

Times(s)


Set5-01 (335.14)

Set5-03 (332.01)

Set5-02 (332.40) )

Set5-04 (318.01)

Set5-05 (311.35)

51

4.1.3. Forming limit of welded seam

During ERW tube production, the two edges are welded together by electrical resistance welding (ERW). Because of low quality control of electrical resistance welding process, some specimens burst at welded seam as show in figure 4.14.

a.) loading path of the formed product of specimens that burst at welded seam

b.) Results of the formed product of specimens that burst at welded seam

Figure 4.14 The specimens that burst at welded seam and corresponding load path.

0

50

100

150

200

250

300

350

0 1 2 3 4 5 6 7 8

Set1Set2Set3Set4

Set1 Set2 Set4 Set3

Intern

al Pre

ssure

(bar)


52

4.2. Grid Measurement

In order to measure the real deformed length, the grid curvatures are investigated. The digital camera with macro lens is used to capture the shape of bulge tube, which is later used to approximate the curve by CAD software as the result is showed in Table 4.1.

Table 4.1 Grid curvature Set Run 𝑟 𝑟 1 1 95.2175 36.8570 2 111.8699 35.5000 3 260.1080 32.7015 4 863.1291 30.7527 5 1456.1444 30.3203 2 1 54.6678 40.5605 2 88.6139 36.5553 4 157.6746 34.7538 5 173.8332 33.9585 3 360.0374 32.0960 6 514.7792 32.0887 3 1 51.39249147 43.2423 2 86.16709075 38.2036 3 83.61262799 38.1561 4 150.5854701 36.294 5 105.4080411 37.373 6 765.8 34.6598 7 314.9241262 34.416 8 598.1552901 32.1596 9 927.0110544 32.0876 4 1 38.49829642 47.425 2 81.53996599 42.3095 3 298.443686 38.0171 4 68.16383701 37.7564 6 234.4953112 37.7758 7 511.2414966 35.301 8 191.229983 36.8714 9 371.9837746 33.4005 10 392.3137255 32.3129 5 1 17.3043 86.01104 2 17.3024 86.21883 3 18.5348 86.23345 4 16.3601 259.3944 5 15.7954 863.2979

53

The deformed grid is measured ± 45 degrees around the welding line as shown in Figure 4.15.

Figure 4.15 Measure zone covering ±45 degrees from welding seam

4.3. Construction of the Forming Limit Curve(FLC)

The critical major and minor strains are plotted to construct the forming limit curve (FLC). Figure 4.16 show forming limit curve and the major and minor strains of all specimens covering ±45 degrees from the weld line.

Figure 4.16 FLC with the major and minor strains of all specimens covering ±45 degrees from welding seam

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

-0.3000 -0.2000 -0.1000 0.0000 0.1000 0.2000 0.3000

Set1

Set2

Set3

Set4

Set5

Welding seam Ma

jor str

ain (ε

1)

Minor strain (ε2)

54

The deformed characteristic of specimens from welding line to 35 degrees is showed in Figure 4.17. The major and minor strains are smallest at 0-7.5 degrees from welding line, then increasing at 7.5-20 degrees and maintain at 20-35 degree. As a result, the maximum strain between 20 and 35 degree is the representation of strain between 35 and 90 degrees.

a.) The Set4 major strain with degree from welding line

b.) The Set4 minor strain with degree from welding line

Figure 4.17 The major and minor strain with degree from welding line of Set4

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 5 10 15 20 25 30 35

Set4-01

Set4-02

Set4-03

Set4-04

Set4-05

Set4-06

Set4-07

Set4-08

Set4-09

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

00 5 10 15 20 25 30 35

Set4-01

Set4-02

Set4-03

Set4-04

Set4-05

Set4-06

Set4-07

Set4-08

Set4-09

Major

strain

(ε1)

Mino

r stra

in (ε

2)

Degree from welding line (Degree)

Degree from welding line (Degree)

Bursting Point

Bursting Point

55

Several researchers (Jieshi Chen, Xianbin Zhou and Jun Chen, 2009) have shown experimentally that non-linear strain path can change the shape and location of the FLC. Nevertheless, to an extent, this effect on the FLC can be minor of the non linearity is kept small. In order to obtain a standardized assessment of the forming limit curve, the strain path at the apex of the bulged sample has to be control as linear as possible(i.e., constant strain ratio). The strain paths at the pole of the forming tube for different strain ratios are shown in the figures 4.18-4.22.

Figure 4.18 Set1 strain path at 30 degree

Apparently, the least feeding distance used to express the excessive pressure which more than expandability of welding line, consequently the burst appeared at the welding line before a material localized necking appeared; therefore, the critical strain at above condition could not reach to real critical strain.

-0.029821, 0.332867

-0.022583, 0.294567

-0.016905, 0.168228

-0.009568, 0.117859 -0.006455, 0.100914

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

-0.035 -0.03 -0.025 -0.02 -0.015 -0.01 -0.005 0

Major

strai

n(ε 1

)

Minor strain (ε2)

56

Figure 4.19 Set2 strain path at burst degree (20 Degree) from welding line

Figure 4.20 Set3 strain path at burst degree (22.5 Degree) from welding line

-0.081826, 0.396554

-0.064544, 0.309325

-0.046852, 0.221205 -0.030791, 0.196836

-0.025699, 0.155908 -0.023716, 0.150363

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

-0.09 -0.08 -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0

-0.153728, 0.516244

-0.100115, 0.340194 -0.109136, 0.346881

-0.106993, 0.285894 -0.083922, 0.317880

-0.070028, 0.226484 -0.070318, 0.227180

-0.043085, 0.142539 -0.039062, 0.157377

0

0.1

0.2

0.3

0.4

0.5

0.6

-0.18 -0.16 -0.14 -0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0

Major

strai

n (ε 1

)

Minor strain (ε2)

Major

strai

n (ε 1

)

Minor strain (ε2)

57

Figure 4.21 Set4 strain path at burst degree (27.5 Degree) from welding line

Figure 4.22 Set5 strain path at burst degree (25 Degree) from welding line

-0.238818, 0.659100

-0.157375, 0.450786

-0.124211, 0.284021 -0.119721, 0.314686

-0.114675, 0.315154 -0.103640, 0.316034

-0.097549, 0.236801 -0.075012, 0.203583

-0.048021, 0.159593

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

-0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0

0.051891347, 0.356595627

0.046204714, 0.352134881

0.039244886, 0.345964341

0.031308471, 0.203006774

0.009871323, 0.132266279

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 0.01 0.02 0.03 0.04 0.05 0.06

Major

strai

n (ε 1

)

Minor strain (ε2)

Minor strain (ε2)

Major

strai

n (ε 1

)

58

From the experimental data, the FLD and forming limit curves (FLC) of STKM 11A tubes are constructed as shown in Figure 4.23. The strain paths at the pole of the forming tube for different strain ratios are also shown in the figure. The four strain paths are obtained from experimental data. As the approximate trend lines, the strain paths at the pole of the forming tube for different strain ratios have a trend line of data as linear. The critical strain from the experimental data and the analytical results, the FLD and forming limit curves (FLC) of STKM 11A tubes are constructed as shown in Figure 4.23.

Figure 4.23 The Experimental FLD and forming limit curves (FLC) of STKM 11A tubes

The weld seam in a tube leads to an obvious non-homogeneity in material properties, and the formability of the weld seam and its heat-affected zone is usually lower than that of the tube, so that tube failures occur closely or on the weld line as shown in Figure 4.23.

-0.081826, 0.396554

-0.153728, 0.516244

-0.238818, 0.659100

-0.029821, 0.332867 0.051891, 0.356596

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1

Major

strai

n (ε 1

)

Minor strain (ε2)

At 27.5˚ from the weld seam

At 22.5˚ from the weld seam

At 20˚ from the weld seam



Forming Limit Diagram

Forming Limit Diagram of low quality weld seam tube

CHAPTER 5

COMPARISON AND VERIFICATION

5.1 Empirical FLC, Analytical FLC and Experimental FLC

The formulation of plastic instability criteria and Keeler’s formula are analytical FLC

and empirical FLC which are used to compare with the experimental FLC, see Figure 5.1. The

formulations used are given in chapter 2. The n value of the flow stress obtained from tensile tests

is used to construct the analytical and empirical FLC of STKM 11A tubes. From the chart, the

experimental FLC is quite close to the Keeler’s formula. The Formulation of plastic instability

criteria gives the lowest FLC.

Figure 5.1 Comparison of predicted forming limit strains with the experimental forming limit

strains for low carbon steels STKM 11A.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

-0.3 -0.2 -0.1 0 0.1 0.2 0.3

Keeler’s formula

Formulation of plastic instability criteria

Experimental FLC

Major

strai

n (ε 1

)

Minor strain (ε2)

60

Figure 5.2 Effects of the r value on the forming limit curve with Hill’s non-quadratic yield

function.

Figure 5.3 Effects of the n value on the forming limit curve with Hill’s non-quadratic yield

function.

Analytical and empirical FLC can be influenced significantly by material properties used.

Figure 5.2 shows the effect of the normal anisotropy of the material, r, on the forming limit curve,

using Hill’s non-quadratic yield function with m= 2.0 and n = 0.2. A larger r value can give a

small raise to the forming limit curve in the tensile–tensile strain region as shown in Figure 5.2. In

the tensile–compressive strain region, however, the forming limit curves are not influenced by the

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

-0.2 -0.2 -0.1 -0.1 0.0 0.1 0.1

r=1.00, n=0.2

r=1.75, n=0.2

r=2.50, n=0.2

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

-0.2 -0.2 -0.1 -0.1 0.0 0.1 0.1

r=1.75, n=0.2

r=1.75, n=0.3

r=1.75, n=0.4

61

r value. It seems that the forming limit curves in the tensile–compressive strain region using

Hill’s localized necking criterion are not influenced by the m and r values in the Hill’s non-

quadratic yield function.

Figure 5.3 shows the effects of the strain-hardening exponent of the tube material, n, on

the forming limit curves using Hill’s nonquadratic yield function with m= 2 and r = 1.75. It is

apparent that the forming limit curves are influenced significantly by the n value. A material with

a larger n value undergoes larger plastic deformation before necking occurs, accordingly a larger

n value raises the forming limit curves. Based on its formulation, however, it is apparent that the

forming limit curve by the formulation of plastic instability criteria is not dependent on the

material thickness.

As a result of Comparison of predicted forming limit strains with the experimental

forming limit strains for low carbon steels STKM 11A, the Keeler’s FLC lies above the

formulation of plastic instability criteria and lies below the experimental FLC. Swift’s diffused

necking criterion and Hill’s localized necking criterion associated with Hill’s non-quadratic yield

function are developed to derive the critical principal strains at the onset of plastic instability,

while the predicted strains at the onset of necking are always smaller than the values measurable

or invisible of the neck size. In practical manufacturing, only visible defects are monitored. For

this reason, the formulation of plastic instability criteria FLC always underestimates the tube’s

visible formability and is over conservative to evaluate the forming severity of parts.

Figure 5.4 Effects of the t value on forming limit curve with Keeler’s formula.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

-0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1

t=1.0, n=0.2

t=1.2, n=0.2

t=1.4, n=0.2

62

Figure 5.5 Effects of the n value on the forming limit curve with Keeler’s formula.

Figure 5.4 shows the effects of the thickness, t, on the forming limit curve, using Keeler’s

formula with n = 0.2. Accordingly, a larger t value can raise the position of forming limit curve as

shown in Figure 5.4. Figure 5.5 shows the effects of the strain-hardening exponent of the tube

material, n, on the forming limit curves using Keeler’s formula t = 1.2. It is apparent that the

forming limit curves are influenced significantly by the n value.

5.2 Verification of Experimental FLC

5.2.1 Verification of experimental FLC with actual bulge test load path

A specimen in set 4 run number 01 was selected to verify the experimental FLC.

An actual load path and real material properties(Experimental FLC, k, r and 𝑛 value) were put to

test in numerical simulation (Finite Element software: DYNAFORM). The results were found

that the final tube in numerical simulation is closely shaped with the formed tube in real

experiment as shown in figure 5.6.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

-0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1

t=1.2, n=0.2

t=1.2, n=0.3

t=1.2, n=0.4

63

a.) Results of the formed product for experiment and numerical simulation

b.) Comparison of major and minor strain for experiment and numerical simulation

Figure 5.6 Results of comparison for experiment and numerical simulation

During simulations, a elastic-plastic material model considering strain hardening

obtained from tensile tests is used. Symbols (X) and (O) represent the major and minor principal

strains of the mesh where the real experiment and numerical simulation (Finite Element software:

DYNAFORM), respectively. It can be seen that simulated strains closely follow the measured

strains. Therefore, FE model can reasonably simulate hydroforming process.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

-0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1

Experimental FLC

Experiment

Simulation

Burst point

Major

strai

n (ε 1

)

Minor strain (ε2)

64

5.2.2. Verification of Experimental FLC with a real automotive part

The forming limit curves determined for these tubular materials were put to test

in formability evaluations of test parts forming in both real experiment and numerical simulation

(Finite Element software: DYNAFORM ). A real automotive part, i.e. a fuel filler pipe (see

Figure 5.7), was considered in this study to design proper process parameters.

First, FLC of comparable steel sheet available in DYNAFORM was used to

conduct all the simulation runs and burst, shown in Figure 5.8.

Figure 5.7 A fuel filler pipe geometry.

Figure 5.8 A final product of fuel filler pipe.

An actual fuel filler pipe load path was put to test in numerical simulation (Finite

Element software: DYNAFORM). The results were found that the final tube in numerical

simulation is closely shaped with the formed tube in real experiment as show in figure 5.9. Figure

5.10 provides a correlation between data points measured experimentally from strain grid of fuel

filler pipe. The predicted FLCs provided from plastic instability criteria and Keeler’s formula is

plotted in the true axial strain versus the true circumferential strain space. The experiment data

65

and simulation data of strain grid analysis for fuel filler pipe are plotted as discrete points in the

same figure. As observed in Figure 5.10, the experiment data is close to simulation data and close

to the experimental FLC. It can be seen that all the measured strains near the crack site are located

above the experimental FLC. Also, none of the critical strains (Crack) lie between the

experimental FLC and Keeler’s FLC. Therefore, from this comparison, the experimental FLC

seems to be the best FLC to estimate a necking (i.e. crack) of this particular tubular steel material.

Figure 5.9 A simulation model of fuel filler pipe.

Figure 5.10 Comparison of predicted forming limit strains with measured experimental data.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-0.3 -0.2 -0.1 0 0.1 0.2 0.3

Keeler’s formula

Formulation of plastic instability criteria

Experimental FLC

Automotive part(Real Experiment-cracks)

Automotive part(Real Experiment-safe)

Automotive part(Numerical simulation )

Major

strai

n (ε 1

)

Minor strain (ε2)

CHAPTER 6

CONCLUSIONS AND SUGGESTIONS

6.1 Conclusions

In this study, FEA was used to investigate and determine proper FLC testing die insert

geometry, i.e. die entry radius and bulge length, in relation to tube sample geometry, i.e. outer

diameter and tube thickness. It was found that the proper die geometry does not depend on sample

thickness but only on outside diameter of the sample. A FLC testing apparatus has been designed

for commonly used STKM 11A tubing in Thailand. Testing process parameter (loading profiles)

were also determined for conducting the test that guarantees linear strain paths in the deforming

samples. This knowledge can be applied to design proper FLC testing die inserts for other tubing

dimensions. Forming limit curves to be generated using this testing apparatus will be of great

usefulness for Thai industry in designing and producing high strength-to-weight ratioed parts

using tube hydroforming technology.

FEA was also used to determine the loading paths to be implemented by the hydraulic

machine with axial feeding and pressure followed the prescribed loading paths that correspond to

the strain paths with a constant strain ratio at the pole of the forming tube. A forming limit

diagram from forming limit experiments was successfully using an experimental apparatus with

fixed bulge length and a test machine with axial feeding. Analytical forming limit curves were

also constructed using Swift’s diffused and Hill’s localized necking criteria associated with Hill’s

non-quadratic yield function, and Keeler’s formula. From the comparison between the

experimental, analytical, empirical FLCs, it was concluded from using a real THF part that the

experimental FLC seemed to be able to predict the necking best. The main conclusions from this

work can be made as follow.

- A bulge forming apparatus of fixed bulge length and a hydraulic test machine with axial

feeding are designed and used to carry out the bulge tests.

- The loading paths of four different strain paths can generate strain paths with a linear

strain path at the pole of the forming tube.

- The forming limit curve (FLC) of tubular material low carbon steels commonly used in

Thai industry, namely STKM 11A is determined

67

- The forming limit curve (FLC) is verified with real part forming experiments for actual

application accurately seems to be not appropriate for THF.

- The welding line quality of ERW tube in Thai industry is low quality.

6.2 Suggestions for Future Work

Although this work is finished, there are some suggestions to the work for further study

determination of forming limit curves of tubular materials for hydroformability evaluation of

automotive parts

- Study effect of weld line expandability on formability in hydroforming of ERW tubes.

- Improvement of steel tubing production toward proper usage for THF technology.

REFERENCES

1. Ahmetoglu M. Tube hydroforming: current research, applications and need for training.

Journal of Materials Processing Technology 98 (2000) 224-231

2. Altan T. Evaluation of tube formability and material characteristics. Journal of Materials

Processing Technology 98 (2000).

3. Asnafi N. Theoretical and experimental analysis of stroke-controlled tube hydroforming.

Materials Science and Engineering A279 (2000) 95–110

4. Chen J. Sheet metal forming limit prediction based on plastic deformation energy. Journal

of Materials Processing Technology (2009)

5. Chu E. Influences of generalized loading parameters on FLD predictions for aluminum

tube hydroforming. Journal of materials processing technology 196 (2008) 1–9

6. F. Dohmann Hydroforming - a method to manufacture light-weight parts. Journal of

Materials Processing Technology 60 (1996) 669-676

7. Hwang Y.M. Analysis of tube bulge forming in an open die considering anisotropic effects

of the tubular material. International Journal of Machine Tools & Manufacture 46 (2006)

1921–1928

8. Hwang Y.M. Forming limit diagrams of tubular materials by bulge tests. Journal of

Materials Processing Technology (2009).

9. Kang S.B. Analytical and numerical approach to prediction of forming limit in tube

hydroforming. International Journal of Mechanical Sciences 47 (2005) 1023–1037

10. Koc M. Hydroforming for advanced manufacturing. Woodhead publishing in materials

11. Koc M. On the characteristics of tubular materials for hydroforming experimentation and

analysis. International Journal of Machine Tools & Manufacture 41 (2001) 761–772

12. Koc M. Prediction of forming limits and parameters in the tube hydroforming process.

International Journal of Machine Tools & Manufacture 42 (2002) 123–138

13. Lei P.L. Bursting failure prediction in tube hydroforming processes by using rigid–plastic

FEM combined with ductile fracture criterion. International Journal of Mechanical Sciences

44 (2002) 1411–1428

14. Nefussi G. Coupled bucklingand plastic instability for tube hydroforming. International

Journal of Mechanical Sciences 44 (2002) 899–914

69

15. Sonobe O. Effect of Mechanical Properties on Formability in Hydroforming of ERW

tubes. JFE STEEL Corp., Steel Research Labs., JAPAN

16. Takuda H. Finite element analysis of limit strains in biaxial stretching of sheet metals

allowing for ductile fracture. International Journal of Mechanical Sciences 42 (2000) 785-798

17. Takuda H. Prediction of forming limit in bore-expanding of sheet metals using ductile

fracture criterion. Journal of Materials Processing Technology 92-93 (1999) 433-438

18. Takuda H. The application of some criteria for ductile fracture to the prediction of the

forming limit of sheet metals. Journal of Materials Processing Technology 95 (1999) 116-121

19. Vollertsen F. On possibilities for the determination of the coefficient of friction in

hydroforming of tube. Journal of Materials Processing Technology 125-126 (2002) 412-420.

20. Xing H.L. Numerical analysis and design for tubular hydroforming. International Journal of

Mechanical Sciences 43 (2001) 1009}1026

21. Yannis P. Inflation and burst of anisotropic aluminum tubes for hydroforming

applications. International Journal of Plasticity 24 (2008) 509–543

22. Yoshida K. Effect of strain hardening behavior on forming limit stresses of steel tube

subjected to nonproportional loading paths. International Journal of Plasticity 23 (2007)

1260–1284

APPENDIX A

2nd INTERNATIONAL CONFERENCE ON GREEN

AND SUSTAINABLE INNOVATION 2009 Appendix A-1: Determination of forming limit curves of tubular materials for

hydroformability evaluation of automotive parts

71

72

73

74

75

76

77

78

APPENDIX B DATA ANALYSIS

Curve Correction

𝑙 = 2𝑟 sin

𝑙 = 2𝑟 sin

Where 𝑙 = Major deformation 𝑙 = Minor deformation 𝑙 ′ = Captured major deformation 𝑙 ′ = Captured minor deformation 𝑟 = Meridian radius of curvature at the pole 𝑟 = Circumferential radius of curvature at the pole

Strain

ε = ln

ε = ln Where ε = Major strain ε = Minor strain d = Initial grid length

80

Set1 No. 𝑟 𝑟 Position L1' L2' L L1 L2 ε ε ξ

1 18.43 95.22 -47.5 3.573 2.653 2.72 3.5786 2.6531 0.2743 -0.0249 -0.0908

-35 3.6 2.64 2.72 3.6057 2.6401 0.2819 -0.0298 -0.1058

-22.5 3.72 2.64 2.72 3.7263 2.6401 0.3148 -0.0298 -0.0947

-10 3.427 2.65 2.72 3.4320 2.6501 0.2325 -0.0260 -0.1120

2.5 3.42 2.65 2.72 3.4249 2.6501 0.2304 -0.0260 -0.1130

15 3.627 2.66 2.72 3.6329 2.6601 0.2894 -0.0223 -0.0770

30 3.933 2.64 2.72 3.9405 2.6401 0.3707 -0.0298 -0.0805

42.5 3.653 2.65 2.72 3.6590 2.6501 0.2966 -0.0260 -0.0878

2 17.75 111.87 -37.5 3.587 2.66 2.72 3.5931 2.6601 0.2784 -0.0223 -0.0800

-25 3.601 2.66 2.72 3.6072 2.6601 0.2823 -0.0223 -0.0789

-12.5 3.533 2.668 2.72 3.5389 2.6681 0.2632 -0.0193 -0.0733

0 3.294 2.67 2.72 3.2987 2.6701 0.1929 -0.0185 -0.0961

15 3.467 2.673 2.72 3.4725 2.6731 0.2443 -0.0174 -0.0713

27.5 3.68 2.658 2.72 3.6866 2.6581 0.3041 -0.0230 -0.0758

40 3.76 2.66 2.72 3.7671 2.6601 0.3257 -0.0223 -0.0684

3 16.35 260.11 -40 3.307 2.68 2.72 3.3127 2.6800 0.1971 -0.0148 -0.0751

-27.5 3.2 2.68 2.72 3.2051 2.6800 0.1641 -0.0148 -0.0902

-15 3.32 2.667 2.72 3.3257 2.6670 0.2011 -0.0197 -0.0978

-2.5 2.973 2.68 2.72 2.9771 2.6800 0.0903 -0.0148 -0.1640

10 3.281 2.665 2.72 3.2865 2.6650 0.1892 -0.0204 -0.1079

22.5 3.254 2.667 2.72 3.2594 2.6670 0.1809 -0.0197 -0.1087

35 3.173 2.67 2.72 3.1780 2.6700 0.1556 -0.0185 -0.1192

45 3.267 2.665 2.72 3.2725 2.6650 0.1849 -0.0204 -0.1105

4 15.38 863.13 -37.5 3.053 2.69 2.72 3.0580 2.6900 0.1171 -0.0111 -0.0947

-25 3.055 2.693 2.72 3.0600 2.6930 0.1178 -0.0100 -0.0847

-12.5 3.08 2.7 2.72 3.0852 2.7000 0.1260 -0.0074 -0.0586

0 2.872 2.7 2.72 2.8762 2.7000 0.0558 -0.0074 -0.1322

12.5 3.08 2.7 2.72 3.0852 2.7000 0.1260 -0.0074 -0.0586

25 3.067 2.694 2.72 3.0721 2.6940 0.1217 -0.0096 -0.0789

37.5 3.04 2.7 2.72 3.0450 2.7000 0.1129 -0.0074 -0.0654

5 15.16 1456.14 -37.5 3.053 2.701 2.72 3.0582 2.7010 0.1172 -0.0070 -0.0598

-25 3.008 2.701 2.72 3.0130 2.7010 0.1023 -0.0070 -0.0685

-12.5 3 2.704 2.72 3.0049 2.7040 0.0996 -0.0059 -0.0592

0 2.84 2.712 2.72 2.8442 2.7120 0.0446 -0.0029 -0.0660

12.5 2.933 2.703 2.72 2.9376 2.7030 0.0770 -0.0063 -0.0815

25 2.987 2.701 2.72 2.9919 2.7010 0.0953 -0.0070 -0.0736

35 2.977 2.707 2.72 2.9818 2.7070 0.0919 -0.0048 -0.0521

81


1 20.28 54.67 -45 3.908 2.5 2.72 3.9141 2.5002 0.3639 -0.0843 -0.2315

-35 3.6 2.64 2.72 3.6057 2.6401 0.2819 -0.0298 -0.1058

-22.5 3.72 2.64 2.72 3.7263 2.6401 0.3148 -0.0298 -0.0947

-10 3.427 2.65 2.72 3.4320 2.6501 0.2325 -0.0260 -0.1120

2.5 3.42 2.65 2.72 3.4249 2.6501 0.2304 -0.0260 -0.1130

15 3.627 2.66 2.72 3.6329 2.6601 0.2894 -0.0223 -0.0770

30 3.933 2.64 2.72 3.9405 2.6401 0.3707 -0.0298 -0.0805

42.5 3.653 2.65 2.72 3.6590 2.6501 0.2966 -0.0260 -0.0878

2 17.75 111.87 -37.5 3.587 2.66 2.72 3.5931 2.6601 0.2784 -0.0223 -0.0800

-25 3.601 2.66 2.72 3.6072 2.6601 0.2823 -0.0223 -0.0789

-12.5 3.533 2.668 2.72 3.5389 2.6681 0.2632 -0.0193 -0.0733

0 3.294 2.67 2.72 3.2987 2.6701 0.1929 -0.0185 -0.0961

15 3.467 2.673 2.72 3.4725 2.6731 0.2443 -0.0174 -0.0713

27.5 3.68 2.658 2.72 3.6866 2.6581 0.3041 -0.0230 -0.0758

40 3.76 2.66 2.72 3.7671 2.6601 0.3257 -0.0223 -0.0684

3 16.35 260.11 -40 3.307 2.68 2.72 3.3127 2.6800 0.1971 -0.0148 -0.0751

-27.5 3.2 2.68 2.72 3.2051 2.6800 0.1641 -0.0148 -0.0902

-15 3.32 2.667 2.72 3.3257 2.6670 0.2011 -0.0197 -0.0978

-2.5 2.973 2.68 2.72 2.9771 2.6800 0.0903 -0.0148 -0.1640

10 3.281 2.665 2.72 3.2865 2.6650 0.1892 -0.0204 -0.1079

22.5 3.254 2.667 2.72 3.2594 2.6670 0.1809 -0.0197 -0.1087

35 3.173 2.67 2.72 3.1780 2.6700 0.1556 -0.0185 -0.1192

45 3.267 2.665 2.72 3.2725 2.6650 0.1849 -0.0204 -0.1105

4 15.38 863.13 -37.5 3.053 2.69 2.72 3.0580 2.6900 0.1171 -0.0111 -0.0947

-25 3.055 2.693 2.72 3.0600 2.6930 0.1178 -0.0100 -0.0847

-12.5 3.08 2.7 2.72 3.0852 2.7000 0.1260 -0.0074 -0.0586

0 2.872 2.7 2.72 2.8762 2.7000 0.0558 -0.0074 -0.1322

12.5 3.08 2.7 2.72 3.0852 2.7000 0.1260 -0.0074 -0.0586

25 3.067 2.694 2.72 3.0721 2.6940 0.1217 -0.0096 -0.0789

37.5 3.04 2.7 2.72 3.0450 2.7000 0.1129 -0.0074 -0.0654

5 15.16 1456.14 -37.5 3.053 2.701 2.72 3.0582 2.7010 0.1172 -0.0070 -0.0598

-25 3.008 2.701 2.72 3.0130 2.7010 0.1023 -0.0070 -0.0685

-12.5 3 2.704 2.72 3.0049 2.7040 0.0996 -0.0059 -0.0592

0 2.84 2.712 2.72 2.8442 2.7120 0.0446 -0.0029 -0.0660

12.5 2.933 2.703 2.72 2.9376 2.7030 0.0770 -0.0063 -0.0815

25 2.987 2.701 2.72 2.9919 2.7010 0.0953 -0.0070 -0.0736

35 2.977 2.707 2.72 2.9818 2.7070 0.0919 -0.0048 -0.0521

82

Set2 (Cont.) No. 𝑟 𝑟 Position L1' L2' L L1 L2 ε ε ξ

6 16.04 514.78 -40 3.173 2.652 2.72 3.1782 2.6520 0.1557 -0.0253 -0.1626

-25 3.2 2.654 2.72 3.2053 2.6540 0.1642 -0.0246 -0.1496

-15 3.107 2.657 2.72 3.1119 2.6570 0.1346 -0.0234 -0.1741

0 3.067 2.659 2.72 3.0717 2.6590 0.1216 -0.0227 -0.1865

15 3.093 2.657 2.72 3.0978 2.6570 0.1301 -0.0234 -0.1802

25 3.227 2.657 2.72 3.2325 2.6570 0.1726 -0.0234 -0.1358

40 3.16 2.653 2.72 3.1651 2.6530 0.1516 -0.0249 -0.1646

Set3

No. 𝑟 𝑟 Position L1' L2' L L1 L2 ε ε ξ 1 21.62 51.39 -45.0 4.51 2.36 2.72 4.5152 2.3632 0.5068 -0.1406 -0.2774

-32.5 4.61 2.34 2.72 4.6228 2.3402 0.5304 -0.1504 -0.2836

-20.0 4.72 2.32 2.72 4.7294 2.3152 0.5532 -0.1611 -0.2913

-7.5 3.93 2.35 2.72 3.9384 2.3502 0.3702 -0.1461 -0.3948

5.0 3.97 2.35 2.72 3.9786 2.3542 0.3803 -0.1444 -0.3798

17.5 4.16 2.36 2.72 4.1664 2.3612 0.4264 -0.1415 -0.3317

30.0 4.80 2.32 2.72 4.8099 2.3202 0.5700 -0.1590 -0.2789

42.5 4.44 2.36 2.72 4.4478 2.3602 0.4918 -0.1419 -0.2885

2 19.10 86.17 -37.5 3.88 2.44 2.72 3.8867 2.4431 0.3569 -0.1074 -0.3008

-25.0 3.87 2.45 2.72 3.8726 2.4541 0.3533 -0.1029 -0.2912

-12.5 3.80 2.46 2.72 3.8063 2.4571 0.3360 -0.1017 -0.3025

2.5 3.63 2.46 2.72 3.6325 2.4641 0.2893 -0.0988 -0.3416

15.0 3.67 2.47 2.72 3.6727 2.4671 0.3003 -0.0976 -0.3250

30.0 3.90 2.47 2.72 3.9018 2.4671 0.3608 -0.0976 -0.2705

42.5 3.89 2.43 2.72 3.8998 2.4301 0.3603 -0.1127 -0.3128

3 19.08 83.61 -37.5 3.83 2.43 2.72 3.8334 2.4341 0.3431 -0.1111 -0.3237

-25.0 3.88 2.44 2.72 3.8877 2.4371 0.3572 -0.1098 -0.3075

-12.5 3.55 2.45 2.72 3.5521 2.4531 0.2669 -0.1033 -0.3870

0.0 3.51 2.47 2.72 3.5120 2.4671 0.2555 -0.0976 -0.3819

12.5 3.77 2.45 2.72 3.7792 2.4541 0.3289 -0.1029 -0.3128

25.0 3.90 2.43 2.72 3.9028 2.4331 0.3611 -0.1115 -0.3087

37.5 3.80 2.43 2.72 3.8063 2.4331 0.3360 -0.1115 -0.3317

4 18.15 150.59 -40.0 3.72 2.44 2.72 3.7265 2.4400 0.3148 -0.1086 -0.3450

-27.5 3.72 2.45 2.72 3.7265 2.4540 0.3148 -0.1029 -0.3268

-15.0 3.40 2.45 2.72 3.4050 2.4540 0.2246 -0.1029 -0.4581

-2.5 3.36 2.47 2.72 3.3648 2.4700 0.2127 -0.0964 -0.4531

10.0 3.52 2.46 2.72 3.5255 2.4570 0.2594 -0.1017 -0.3920

22.5 3.64 2.43 2.72 3.6461 2.4340 0.2930 -0.1111 -0.3791

35.0 3.71 2.43 2.72 3.7145 2.4270 0.3116 -0.1140 -0.3657

83

Set3 (Cont.) No. 𝑟 𝑟 Position L1' L2' L L1 L2 ε ε ξ

5 18.69 105.41 -45.0 3.69 2.48 2.72 3.6990 2.4801 0.3074 -0.0924 -0.3004

-32.5 3.72 2.49 2.72 3.7262 2.4901 0.3147 -0.0883 -0.2806

-20.0 3.67 2.51 2.72 3.6729 2.5101 0.3004 -0.0803 -0.2674

-7.5 3.41 2.51 2.72 3.4178 2.5051 0.2284 -0.0823 -0.3605

7.5 3.47 2.51 2.72 3.4720 2.5071 0.2441 -0.0815 -0.3340

20.0 3.80 2.50 2.72 3.8066 2.4951 0.3361 -0.0863 -0.2568

32.5 3.73 2.50 2.72 3.7392 2.5001 0.3182 -0.0843 -0.2649

45.0 3.78 2.50 2.72 3.7814 2.5001 0.3295 -0.0843 -0.2559

6 17.33 765.80 -40.0 3.43 2.52 2.72 3.4326 2.5230 0.2327 -0.0752 -0.3231

-27.5 3.43 2.55 2.72 3.4326 2.5470 0.2327 -0.0657 -0.2824

-15.0 3.33 2.55 2.72 3.3392 2.5490 0.2051 -0.0649 -0.3166

0.0 3.36 2.55 2.72 3.3653 2.5530 0.2129 -0.0634 -0.2976

12.5 3.41 2.53 2.72 3.4185 2.5270 0.2286 -0.0736 -0.3220

27.5 3.43 2.52 2.72 3.4326 2.5230 0.2327 -0.0752 -0.3231

40.0 3.41 2.53 2.72 3.4185 2.5270 0.2286 -0.0736 -0.3220

7 17.21 314.92 -45.0 3.36 2.54 2.72 3.3654 2.5370 0.2129 -0.0696 -0.3271

-32.5 3.40 2.53 2.72 3.4056 2.5300 0.2248 -0.0724 -0.3221

-20.0 3.40 2.54 2.72 3.4056 2.5350 0.2248 -0.0704 -0.3134

-7.5 3.25 2.55 2.72 3.2579 2.5530 0.1804 -0.0634 -0.3511

7.5 3.35 2.55 2.72 3.3523 2.5500 0.2090 -0.0645 -0.3088

20.0 3.43 2.54 2.72 3.4327 2.5370 0.2327 -0.0696 -0.2993

32.5 3.37 2.54 2.72 3.3794 2.5350 0.2171 -0.0704 -0.3245

45.0 3.39 2.53 2.72 3.3925 2.5340 0.2209 -0.0708 -0.3206

8 16.08 598.16 -40.0 3.15 2.60 2.72 3.1520 2.6020 0.1474 -0.0444 -0.3008

-25.0 3.16 2.61 2.72 3.1651 2.6100 0.1516 -0.0413 -0.2724

12.5 3.05 2.60 2.72 3.0586 2.6000 0.1173 -0.0451 -0.3846

0.0 3.00 2.62 2.72 3.0044 2.6200 0.0994 -0.0375 -0.3767

12.5 3.09 2.61 2.72 3.0978 2.6130 0.1301 -0.0401 -0.3086

25.0 3.13 2.60 2.72 3.1380 2.6000 0.1429 -0.0451 -0.3156

40.0 3.12 2.60 2.72 3.1249 2.5970 0.1388 -0.0463 -0.3334

9 16.04 927.01 -45.0 3.15 2.61 2.72 3.1521 2.6140 0.1474 -0.0397 -0.2696

-32.5 3.16 2.61 2.72 3.1651 2.6130 0.1516 -0.0401 -0.2648

-20.0 3.16 2.62 2.72 3.1651 2.6150 0.1516 -0.0394 -0.2597

-7.5 2.99 2.62 2.72 2.9913 2.6170 0.0951 -0.0386 -0.4060

7.5 3.09 2.61 2.72 3.0978 2.6070 0.1301 -0.0424 -0.3262

20.0 3.21 2.62 2.72 3.2184 2.6170 0.1683 -0.0386 -0.2294

32.5 3.13 2.62 2.72 3.1380 2.6170 0.1430 -0.0386 -0.2700

45.0 3.15 2.61 2.72 3.1521 2.6140 0.1474 -0.0397 -0.2696

84


1 23.71 38.50 -45.0 4.84 2.23 2.72 4.8484 2.2303 0.5780 -0.1985 -0.3434

-32.5 5.19 2.16 2.72 5.1974 2.1603 0.6475 -0.2304 -0.3558

-20.0 5.23 2.15 2.72 5.2366 2.1543 0.6550 -0.2332 -0.3560

-7.5 4.33 2.20 2.72 4.3401 2.1973 0.4673 -0.2134 -0.4567

7.5 4.00 2.20 2.72 4.0048 2.2023 0.3869 -0.2111 -0.5458

20.0 4.69 2.15 2.72 4.7007 2.1543 0.5471 -0.2332 -0.4262

32.5 5.73 2.11 2.72 5.7471 2.1083 0.7481 -0.2548 -0.3406

45.0 4.93 2.17 2.72 4.9419 2.1733 0.5971 -0.2244 -0.3758

2 21.15 81.54 -45.0 4.20 2.31 2.72 4.2069 2.3081 0.4361 -0.1642 -0.3766

-32.5 4.25 2.33 2.72 4.2612 2.3331 0.4489 -0.1534 -0.3418

-20.0 4.19 2.35 2.72 4.1939 2.3481 0.4330 -0.1470 -0.3396

-7.5 3.84 2.32 2.72 3.8453 2.3231 0.3462 -0.1577 -0.4556

7.5 3.87 2.37 2.72 3.8734 2.3671 0.3535 -0.1390 -0.3931

20.0 4.20 2.31 2.72 4.2069 2.3071 0.4361 -0.1647 -0.3776

32.5 4.36 2.31 2.72 4.3708 2.3101 0.4743 -0.1634 -0.3444

45.0 4.36 2.29 2.72 4.3698 2.2911 0.4741 -0.1716 -0.3620

3 19.01 298.44 -45.0 3.76 2.41 2.72 3.7682 2.4070 0.3260 -0.1222 -0.3750

-32.5 3.71 2.41 2.72 3.7129 2.4080 0.3112 -0.1218 -0.3915

-20.0 3.80 2.42 2.72 3.8064 2.4230 0.3360 -0.1156 -0.3441

-7.5 3.35 2.42 2.72 3.3513 2.4230 0.2087 -0.1156 -0.5539

7.5 3.51 2.43 2.72 3.5120 2.4270 0.2556 -0.1140 -0.4460

20.0 3.68 2.42 2.72 3.6858 2.4200 0.3038 -0.1169 -0.3846

32.5 3.71 2.41 2.72 3.7129 2.4070 0.3112 -0.1222 -0.3929

45.0 3.72 2.41 2.72 3.7260 2.4100 0.3147 -0.1210 -0.3845

4 18.88 68.16 -45.0 3.73 2.39 2.72 3.7391 2.3911 0.3182 -0.1289 -0.4050

-32.5 3.63 2.42 2.72 3.6336 2.4201 0.2896 -0.1168 -0.4034

-20.0 3.69 2.39 2.72 3.6989 2.3891 0.3074 -0.1297 -0.4219

-7.5 3.45 2.41 2.72 3.4578 2.4101 0.2400 -0.1210 -0.5040

7.5 3.40 2.42 2.72 3.4046 2.4201 0.2245 -0.1168 -0.5203

20.0 3.51 2.41 2.72 3.5121 2.4071 0.2556 -0.1222 -0.4781

32.5 3.60 2.39 2.72 3.6055 2.3901 0.2818 -0.1293 -0.4588

45.0 3.75 2.40 2.72 3.7532 2.3971 0.3220 -0.1264 -0.3925

5 18.89 234.50 -45.0 3.80 2.42 2.72 3.8064 2.4200 0.3361 -0.1169 -0.3477

-32.5 3.65 2.42 2.72 3.6597 2.4200 0.2968 -0.1169 -0.3938

-20.0 3.75 2.44 2.72 3.7532 2.4350 0.3220 -0.1107 -0.3438

-7.5 3.59 2.45 2.72 3.5924 2.4450 0.2782 -0.1066 -0.3831

7.5 3.52 2.44 2.72 3.5251 2.4370 0.2593 -0.1099 -0.4237

20.0 3.76 2.42 2.72 3.7672 2.4240 0.3257 -0.1152 -0.3537

32.5 3.75 2.43 2.72 3.7532 2.4250 0.3220 -0.1148 -0.3565

45.0 3.76 2.42 2.72 3.7662 2.4210 0.3254 -0.1164 -0.3578

85

Set4(Cont.) No. 𝑟 𝑟 Position L1' L2' L L1 L2 ε ε ξ

6 18.44 191.23 -45.0 3.72 2.45 2.72 3.7273 2.4510 0.3151 -0.1041 -0.3305

-32.5 3.67 2.45 2.72 3.6731 2.4500 0.3004 -0.1045 -0.3480

-20.0 3.73 2.45 2.72 3.7394 2.4540 0.3183 -0.1029 -0.3233

-7.5 3.41 2.46 2.72 3.4189 2.4591 0.2287 -0.1008 -0.4409

7.5 3.47 2.46 2.72 3.4721 2.4570 0.2441 -0.1017 -0.4165

20.0 3.71 2.45 2.72 3.7153 2.4540 0.3118 -0.1029 -0.3300

32.5 3.79 2.45 2.72 3.7947 2.4520 0.3330 -0.1037 -0.3115

45.0 3.68 2.45 2.72 3.6861 2.4500 0.3039 -0.1045 -0.3439

7 17.65 511.24 -45.0 3.47 2.47 2.72 3.4726 2.4690 0.2443 -0.0968 -0.3964

-32.5 3.44 2.47 2.72 3.4455 2.4690 0.2364 -0.0968 -0.4095

-20.0 3.40 2.47 2.72 3.4053 2.4740 0.2247 -0.0948 -0.4219

-7.5 3.33 2.47 2.72 3.3380 2.4740 0.2047 -0.0948 -0.4630

7.5 3.29 2.47 2.72 3.2978 2.4740 0.1926 -0.0948 -0.4921

20.0 3.43 2.47 2.72 3.4324 2.4670 0.2326 -0.0976 -0.4197

32.5 3.48 2.46 2.72 3.4857 2.4610 0.2480 -0.1001 -0.4034

45.0 3.47 2.46 2.72 3.4746 2.4620 0.2448 -0.0997 -0.4070

8 16.70 371.98 -37.5 3.32 2.52 2.72 3.3255 2.5240 0.2010 -0.0748 -0.3721

-20.0 3.28 2.52 2.72 3.2853 2.5210 0.1888 -0.0760 -0.4024

-12.5 3.19 2.54 2.72 3.1919 2.5400 0.1600 -0.0685 -0.4280

0.0 3.15 2.56 2.72 3.1517 2.5600 0.1473 -0.0606 -0.4116

12.5 3.24 2.56 2.72 3.2451 2.5600 0.1765 -0.0606 -0.3434

20.0 3.36 2.52 2.72 3.3657 2.5220 0.2130 -0.0756 -0.3548

37.5 3.36 2.53 2.72 3.3667 2.5280 0.2133 -0.0732 -0.3432

9 16.16 392.31 -45.0 3.20 2.58 2.72 3.2063 2.5800 0.1645 -0.0528 -0.3213

-32.5 3.19 2.57 2.72 3.1922 2.5720 0.1601 -0.0559 -0.3495

-20.0 3.19 2.60 2.72 3.1922 2.6000 0.1601 -0.0451 -0.2819

-7.5 3.08 2.59 2.72 3.0847 2.5940 0.1258 -0.0474 -0.3770

7.5 3.03 2.59 2.72 3.0314 2.5930 0.1084 -0.0478 -0.4411

20.0 3.16 2.60 2.72 3.1651 2.6000 0.1515 -0.0451 -0.2977

32.5 3.20 2.60 2.72 3.2053 2.6030 0.1642 -0.0440 -0.2678

45.0 3.16 2.60 2.72 3.1651 2.6040 0.1515 -0.0436 -0.2876

86


1 17.30 86.01 -37.5 3.73 2.85 2.72 3.7413 2.8501 0.3188 0.0467 0.1466

-25.0 4.03 2.85 2.72 4.0361 2.8501 0.3947 0.0467 0.1184

-12.5 3.54 2.85 2.72 3.5462 2.8501 0.2652 0.0467 0.1762

0.0 3.30 2.82 2.72 3.3050 2.8211 0.1948 0.0365 0.1874

12.5 3.69 2.85 2.72 3.7000 2.8541 0.3077 0.0481 0.1564

25.0 2.72

37.5 3.71 2.84 2.72 3.7141 2.8401 0.3115 0.0432 0.1387

2 17.30 86.22 -37.5 3.73 2.81 2.72 3.7403 2.8081 0.3185 0.0319 0.1001

-25.0 4.05 2.83 2.72 4.0623 2.8271 0.4011 0.0386 0.0963

-12.5 3.49 2.83 2.72 3.5000 2.8271 0.2521 0.0386 0.1532

0.0 3.38 2.82 2.72 3.3854 2.8201 0.2188 0.0361 0.1652

12.5 3.51 2.84 2.72 3.5130 2.8401 0.2558 0.0432 0.1689

25.0 2.72

37.5 3.76 2.82 2.72 3.7674 2.8211 0.3258 0.0365 0.1121

3 18.53 86.23 -37.5 3.81 2.88 2.72 3.8198 2.8751 0.3396 0.0555 0.1634

-25.0 2.72

-12.5 3.59 2.87 2.72 3.5926 2.8701 0.2783 0.0537 0.1931

0.0 3.32 2.83 2.72 3.3245 2.8261 0.2007 0.0383 0.1907

12.5 3.45 2.84 2.72 3.4590 2.8401 0.2404 0.0432 0.1798

25.0 4.07 2.86 2.72 4.0752 2.8571 0.4043 0.0492 0.1217

37.5 3.84 2.87 2.72 3.8479 2.8681 0.3469 0.0530 0.1529

4 16.36 259.39 -37.5 3.33 2.80 2.72 3.3388 2.8000 0.2050 0.0290 0.1414

-25.0 3.39 2.80 2.72 3.3931 2.8000 0.2211 0.0290 0.1311

-12.5 3.29 2.80 2.72 3.2986 2.8000 0.1929 0.0290 0.1503

0.0 2.72

12.5 3.25 2.80 2.72 3.2584 2.8000 0.1806 0.0290 0.1605

25.0 3.27 2.81 2.72 3.2725 2.8130 0.1849 0.0336 0.1818

37.5 3.27 2.80 2.72 3.2725 2.8000 0.1849 0.0290 0.1568

5 15.80 863.30 -37.5 2.99 2.73 2.72 2.9915 2.7330 0.0951 0.0048 0.0501

-25.0 3.05 2.74 2.72 3.0578 2.7370 0.1171 0.0062 0.0532

-12.5 2.84 2.71 2.72 2.8438 2.7070 0.0445 -0.0048 -0.1076

0.0 2.80 2.71 2.72 2.8037 2.7070 0.0303 -0.0048 -0.1581

12.5 2.93 2.72 2.72 2.9312 2.7170 0.0748 -0.0011 -0.0148

25.0 3.15 2.76 2.72 3.1522 2.7570 0.1475 0.0135 0.0916

37.5 3.09 2.76 2.72 3.0980 2.7630 0.1301 0.0157 0.1206

APPENDIX C

TOOLING SCHEMATIC

88

89

90

91

92

93

94

95

BIOGRAPHY

Name: Mr. Ramil Kesvarakul

Date of Birth: November 1, 1983

Place of Birth: Bangkok, Thailand

Education:

2003 – 2007 B. Eng. in Industrial Engineering, Department of Industrial

Engineering, Faculty of Engineering, King Mongkut’s Institute

of Technology Ladkrabang (KMITL)

2007 – 2010 M. Eng. in Automotive Engineering (International program),

International College, King Mongkut’s Institute of Technology

Ladkrabang (KMITL)

Scholarships:

2007-2009 Full scholarship for study in the master degree from National

Science and Technology Development Agency (NSTDA)

Publications:

R. Kesvarakul, M. Pimsarn, S. Jirathearanat and N. Ohtake “Determination of forming limit

curves of tubular materials for hydroformability evaluation of automotive parts”, Proceeding of

the 3rd International Conference on Green and Sustainable Innovation 2009, Chiang Rai,

Thailand, December 2nd-4th, 2009. pp 166.

Ramil Paper

Documents

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